Content Writer-SME | Updated On - Oct 14, 2024
The rate of flow of electrons or charge through a cross-section of a wire is called current. In general, we use current and electricity interchangeably. However, in physics, electricity is produced by the flow of current. Thus, current electricity allows the flow of current from one place to another. The constant flow of charged particles such as electrons or ions forms the basis for powering up any kind of electrical and electronic device.
- The formula of electric current is given as \(I = \frac {q} {t}\).
- The SI unit of Electric current is ‘Ampere’.
- The conventional direction of electric current is the direction of motion of the positive charge.
What is Electric Current?
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The electric current is the same for all cross-sections of a conductor of a non-uniform cross-section. The current flows due to the motion of free electrons in a metallic conductor. In electrolytes and ionized gases, current flows due to the motion of electrons and positive ions. If a charge q revolves in a circle over a unit time t, the equivalent electric current is,
\(i = \frac{q}{t}\)
Flow of Current Electricity
Types of Electric current
As per the magnitude and direction of electric current it is of two types i.e,
- Direct Current or DC: When electric current flows from high electron density to low electron density, it is called direct current. In direct current, its magnitude and direction do not change with time. Its sources are battery, cell, or DC dynamo.
- Alternating Current or AC: The flow of electric current in the case of AC is bidirectional. Its magnitude and direction changes continuously and periodically. The common sources of AC are AC Dynamo and household electrical appliances.
Discover about the Chapter video:
Current Electricity Detailed Video Explanation:
Current Density
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Current Density refers to the electric current flowing per unit area of a cross-section of a conductor. Its formulae are \(J = \frac{I}{A}\). Its SI unit is Ampere metre2. It is a vector quantity and it is in the direction of motion positive charge or flow of current.
Thermal Velocity of Free Electrons
When free electrons in a metal move randomly with a very high speed of the order of 105 ms-1. The average thermal velocity of free electrons in any direction remains zero.
Drift Velocity of Free Electrons
When a potential difference is applied across the ends of a conductor, the free electrons in it move with an average velocity opposite to the direction of the electric field. The relationship between the electric current and drift velocity is \(V_d=\frac{I}{A\times n\times e}\)
Mobility
The Drift Velocity of an electron per unit electric field applied. The formula is \(\frac {V_d} {e}\). Its SI unit is m2s-1v-1
Ohm’s Law
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Ohm’s law states that, “electric current flowing through the conductor is directly proportional to the potential difference (V) applied across its ends”. It is written as V=IR
where, R is the electrical resistance of a conductor.
- Ohm’s law gives the relationship between electric current and potential difference.
- Ohm’s law holds only if provided temperature and physical factors remain constant.
- In filament of the light bulb, increasing the current raises the temperature and thus Ohm’s law cannot be applied.
Water Pipe Analogy
Ohm’s law describes current flow through a resistance when different voltages are applied at each end of resistance. It's not possible to see the electrons, therefore the water pipe analogy helps us understand electric circuits in a better way. This analogy is a good mechanical system ie analogous to an electric circuit. Here Voltage is analogous to water pressure, the current is the amount of water flowing through the pipe and resistance is the size of the pipe. More water will flow through a pipe (current) when more pressure is applied (voltage) and bigger is the pipe (low resistance).
Water Pipe Analogy
Calculating Electrical Power using Ohm’s Law
- The rate at which energy is converted from electrical energy of moving charges to other forms like mechanical energy, heat, magnetic fields in electric fields is known as Electric power.
- The unit is the watt.
- When values of voltage and current are given, the power \(P = V\times I\)
- When values for voltage and resistance are given then power \(P = \frac {V^2}{R}\)
- When values for current and resistance are given, then \(P = I^2 \times R\)
Applications of Ohm’s Law
- Ohm’s law helps determine voltage, resistance, or current.
- It is used to maintain desired voltage drop across electronic components.
- Ohm’s law is used in the DC ammeter to divert current.
Limitations of Ohm’s Law
- Ohm’s is not applicable for unilateral electrical elements like diodes and transistors as they allow current to flow only in one direction.
- Non-linear electrical elements like capacitance and resistance, voltage, and current are not constant.
Electrical Resistance
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Electrical Resistance refers to the obstruction offered by any conductor in the path of the flow of current. The formula of resistance is \(R = \frac {V}{I}\). Its SI unit is the ohm. The Electrical resistance of a conductor is given by:
| \(R =ρ \times l\times \bigg(\frac{1}{A}\bigg)\) l is the length of the conductor, A is the cross-section area, ρ is the resistivity of the material of a conductor |
Factors that affect electrical resistance are the Cross-sectional area of the conductor, length of the conductor, the material of the conductor, and temperature of conducting material.
Resistivity
- Resistivity is a qualitative measurement of a material’s ability to resist flowing electric current.
- Insulators have a higher value of resistivity compared to conductors.
- The resistivity of a material of a conductor is given by \(ρ = m\times \bigg(\frac{1}{n^2\times t}\bigg)\).
- It depends on the nature and temperature of the material. Independent of other dimensions like length, area of cross-section, etc.
- It is low for metals, more for semiconductors, and high for alloys like nichrome, constantan, etc.
- In a magnetic field, the resistivity of metals increases but the resistivity of ferromagnetic materials decreases.
How Do Resistors Work?
Electric Resistivity
Electric resistivity is defined as the electrical resistance offered per unit length and unit cross-sectional area at a specific temperature. It is denoted by ρ. It is also known as specific electrical resistance. Its formula is:
| \(ρ = \frac {E} {J}\) E is the electric field, J is the current density |
Electrical resistivity is the reciprocal of electrical conductivity and is a measure of the ability of a material to oppose the flow of current. Metals are good resistors of electricity and thus have low resistivity. Insulators such as rubber, glass, and graphite have high resistivity. Semiconductors resistivity decreases with an increase in temperature and is also affected by the presence of impurities.
Resistivity of Materials
Resistivity of Different Materials
The resistivity of different materials is listed in the table below:
Resistivity of Different Materials
- Formula of Resistivity: The materials with the electric field and current density have the given resistivity formula ie \(ρ = \frac {E} {J}\). Here ρ is the resistivity of the material, E is the magnitude of the electric field and J is the magnitude of current density. Conductors with a uniform cross-section and uniform flow of electric current can use the formula \(ρ =R \times A\bigg(\frac{1}{l}\bigg)\).
- Resistor color coding: The resistance is indicated by using electronic color codes. It contains 4 bands. The first band indicates the first significant figure of resistance, the second band indicates the second significant figure, the third band indicates a decimal multiplier, and the fourth band indicates tolerance that the resistor can withstand. In the absence of the 4th band, a default tolerance of 20% is taken.
Resistor color coding
Series and Parallel Combination
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A resistor is defined as a passive two-terminal electrical component that implements electrical resistance as a circuit element.
Important Notes on Resistors
- They reduce current flow and lower voltage levels within the circuit.
- It is a passive element ie it only consumes power but doesn’t generate.
- A circuit is composed of conductors like wire, power source, load, resistor, and switch.
- It starts and ends at the same point. In general, a copper wire without insulation is used as a conductor.
- In an electric circuit, different components are connected either in series or in parallel to produce different resistive networks.
- In the same circuit, resistors can be connected in both parallel and series across different loops to produce a more complex resistive network known as mixed resistor circuits.
Resistors in series and parallel
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Resistors in Series
Resistors in Parallel
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Cells, Electromotive Force and Internal Resistance
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Electric Cell is a device that converts chemical energy into electrical energy. The battery provides the constant electromotive force to an electrical circuit. Each cell comprises 2 half cells connected in series by a conductive electrolyte containing anions and cations. One-half cell is made of electrolyte and negative electrode called an anion. The other half cell is made of electrolyte and positive electrode called cathode.
Redox reactions occur simultaneously. Cations are reduced at the cathode while charging while anions are oxidized at the anode while charging. Electrodes do not touch each other, they are electrically connected by the electrolyte.
Cells, Electromotive Force and Internal Resistance
Electromotive force (emf) of a cell
- The energy given by a cell in flowing unit positive charge throughout the circuit one time is equal to the emf of a cell.
- When there is no electrical equipment attached to the cell, then the electrolyte has the same potential (emf) throughout the cell.
- Condition of no current flowing through the cell is also known as an open circuit and it results in emf of a cell is equal to the difference in emf of electrodes.
- The potential difference between anode and cathode is known as EMF. It is represented as E =W/q.
- SI unit of electromotive force is volt.
Terminal Potential Difference of a cell
The energy given by a cell in flowing unit positive charge through till outer circuit one time from one terminal of cell to another terminal. It is represented as V = W/q. Its SI unit is volt.
Internal Resistance of a cell
- The obstruction offered by the electrolyte of a cell in the path of electric current.
- The internal resistance of a cell increases with an increase in the concentration of electrolytes.
- It also increases with an increase in distance between electrodes.
- It decreases with an increase in the area of electrodes dipped in the electrolyte.
- The relation between E, V, and r is E=V+Ir. Here r = (E/V-1)R.
- If the cell is in a charging state, then E =V-Ir.
Cells in Series and Parallel
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Kirchhoff’s Rules
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There are two Kirchhoff’s laws to solve complicated electrical circuits. Using these laws and equations for individual components such as a resistor, capacitor, and inductor, we can analyze circuits.
- Junction Rule: The algebraic sum of all currents meeting at a junction in a closed circuit is zero. It follows the law of conservation of charge. In this rule, the total current entering the junction is the same as the charge leaving the junction as there is no charge lost. This current law can be applied to analyze parallel circuits.
- Loop Rule: The algebraic sum of all potential differences or voltage in any closed circuit is zero. It follows the law of conservation of energy. When you start at any point of the loop and continue in the same direction, voltage drops in all directions either negative or positive and returns to the same point. It should be noted that direction should either be maintained clockwise or counterclockwise or else the final voltage value will not be equal to zero. This voltage law is applied to analyze circuits in series.
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Wheatstone BridgeIt is an arrangement of 4 resistances where one resistance is unknown while the rest are known. The bridge is said to be balanced when the deflection of the galvanometer is zero. The principle of the Wheatstone bridge is P/Q = R/S. The value of unknown resistance S can be found using the values of P, Q, and R. Meter BridgeIt is the simplest form of Wheatstone Bridge and is used for comparing resistance accurately. The formula used to compare resistance is R/S = I1/(100 – I1). I1 is the length of the wire and it is from there, that a null point is obtained. |
Potentiometer
It is an ideal device to measure the potential difference between the two points. It consists of long resistance wire AB of the uniform cross-section.
Potentiometer
If R is the total resistance of Potentiometer wire, L is total length, then the potential gradient will be K =V/L =IR/L = Eo R/(Ro + R)L where E0 is emf of battery and R0 is the resistance inserted using rheostat Rh.
Important Topics for JEE Mains 2024-2025Current and Electricity chapter of Class 12 is one of the favorite chapters for those setting JEE Mains exam questions. Both conceptual and numerical questions can be asked from this. Based on the analysis of last five years, we have mentioned three important topics under Current and Electricity chapter of Class 12 that should be covered in more detail before the exam:
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Things to Remember
- The rate of flow of charge through any cross-section of a wire is known as electric current.
- The formulae of electric current (I) =q/t.
- The SI unit of Electric current is Ampere.
- The conventional direction of electric current is the direction of motion of the positive charge.
- As per the magnitude and direction of electric current it is of two types ie Direct Current and Alternating Current.
- The electric current flowing through the conductor is directly proportional to the potential difference (V) applied across its ends.
- Resistivity is a qualitative measurement of a material’s ability to resist flowing electric current.
Previous Year Questions
- If now we hav.e to change the null point at 9th9th wire, what should we do?… [ DUET 2007 ]
- The electrical permittivity and magnetic permeability of free space are… [ DUET 2003 ]
- Just after key K is pressed to complete the circuit, the reading will be …. [ KEAM 1999 ]
- The resistance between any two terminals is when connected in a triangle is…. [ NEET 1993 ]
- potential drop through 4Ω4Ω resistor is… [ NEET 1993 ]
- The potential difference per unit length of the wire will be… [ NEET 1999 ]
- Value of R for which the power delivered in it is maximum is given by... [ NEET 1992 ]
- In a closed circuit, the current II (in ampere) at an instant of time tt (in second) is given by…? [KEAM]
- Five cells each of emf E and internal resistance r send the same amount of current through…? [KEAM]
- Electrical conductivity is the reciprocal of…? [KEAM]
- Consider a cylindrical conductor of Length L and area of cross section A. The specific conductivity…? [KEAM]
- An ammeter, voltmeter and a resistor are connected in series to a cell and the readings are…? [KEAM]
- A potentiometer wire of length 10m and resistance 20Ω is connected in series with a…? [KEAM]
- A potentiometer wire, 10m long, has a resistance of 40Ω. It is connected in series with a…? [KEAM]
- A given resistor has the following colour code of the various strips on it: Brown, black, green…? [KEAM]
- A galvanometer can be converted into an ammeter by connecting…? [KEAM]
- A copper wire with a cross-section area of 2×10−6m2 has a free electron density equal…? [KEAM]
- 4 cells each of emf2 V and internal resistance of 1O are connected in parallel to a load resistor…? [KEAM]
- A circuit is made using R1,R2,R3,R4 and a battery as shown in the following figure. Find the equivalent…? [KEAM]
- A battery of 6V and internal resistance 2Ω is connected to a silver voltameter. If the current of…? [KEAM]
Sample Questions
Ques 1. When electrons gather in a metal from lower to higher potential, does this indicate that all the free electrons of the metal are moving in the same direction? (Delhi 2012)
Ans.
No, all the free electrons of the metal will not move in the same direction. Only the drift velocities of the electrons are superposed over their haphazard thermal velocities. The solid line refers to the random path followed by a free electron in the absence of an external field. The electrons that are moving from A to B are making 6 collisions on its path. When an electric field is applied, the dotted curve shows how the random motion of the same electron gets modified.
Ques 2. A 10 v battery of negligible internal internal resistance is connected across a 200 V and a resistance of 38? as shown in the figure below. Derive the value of the current in circuit. (Delhi 2013)
Ans. By applying Kirchhof’s rule we get,
200 - 10 = 190 V
And I = \(\frac {V} {R}\)= \(\frac {190} {38}\) = 5 A
Ques 3. What do you mean by the term ‘Mobility’ of charge carried in a conductor? Write its S.I. unit. (Delhi 2014)
Ans. Mobility of charge carried in a conductor is defined as the magnitude of the drift velocity per unit electric field E.
Ques 4. Obtain the expression for the current in a conductor of a cross sectional area A in terms of drift velocity. (Comptt. All India 2013)
Ans. Drift velocity can be defined as the velocity of the free electrons with which they drift towards the positive terminal under the influence of an external electric field. The drift velocity of electron is of the order of 10-5 m/sec. Expression for current in terms of drift velocity is, I = Anevd
Assume a conductor of length l and of uniform cross section area A.
Therefore, volume of the conductor AI
Total number of free electrons in the conductor is Aln if n is the number of conductors.
If e is the charge on each electron, then the total charge on all A of the free electrons in the conductor, q = Alne
The electric field set up across the conductor of potential difference V is,
E = \(\frac {V} {I}\)
I = Anevd
For this field, the free electrons in the conductor will begin to move with a drift velocity Vd towards the positive terminal of the battery.
Thus, time taken by the free electrons to cross the conductor,
Since A, n and e are constants
Hence, I ∞ Vd
Hence, the current flowing through a conductor is directly proportional to the drift velocity.
Ques 5. State Kirchhoff’s rule and explain briefly how these rules are justified. (Delhi 2014)
Ans. There are two Kirchhoff’s laws to solve complicated electrical circuits. Using these laws and equations for individual components such as a resistor, capacitor, and inductor, we can analyze circuits.
Junction Rule: The algebraic sum of all currents meeting at a junction in a closed circuit is zero. It follows the law of conservation of charge. In this rule, the total current entering the junction is the same as the charge leaving the junction as there is no charge lost. This current law can be applied to analyze parallel circuits.
Loop Rule: The algebraic sum of all potential differences or voltage in any closed circuit is zero. It follows the law of conservation of energy. When you start at any point of the loop and continue in the same direction, voltage drops in all directions either in negative or positive and returns to the same point.
These two laws are justified on the basis of the law of conservation of charge and the law of conservation of energy respectively.
Ques 6. Obtain the conditions for balance conditions in a Wheatstone bridge by using Kirchhoff’s rules. (Delhi 2015)
Ans. The conditions for the balance condition in a Wheatstone bridge,
By applying Kirchhoff’s loop rule to the closed loop ADBA,
This is the required balance condition in a Wheatstone bridge arrangement.
Ques 7. (a) Obtain the equation between current density J and potential difference V across a current carrying conductor of length area of cross section A and number density of free electrons.
(b) Estimate the average drift speed of conduction electrons in a copper wire of cross sectional area 1.0 x 10-7 m2 carrying a current of 1.5 A [Consider that the number density of conduction electrons is 9 x 1928 m-3]. (Comptt. Delhi 2012)
Ans. (a) Considering a potential difference V is applied across a conductor of length l and of uniform cross section A
The electric field E set up inside the conductor is,
E = V/l
Under the influence of the field , the free electrons drift in the opposite direction with an average drift velocity Vd.
Now, let the number of electrons per unit volume = n
Charge on an electron = e
Number of electrons in length l of the conductor is n x volume of the conductor = n x Al
Total charge in length l of the conductor is
q = enAl … (i)
All electrons which entre the conductor at the right end will pass through the conductor at the left end in time,
Thus, the current density of a metallic conductor is directly proportional to the drift speed of electrons.
(b) 
Ques 8. State the principle of potentiometer.
(i) Write the principle of working potentiometer.
(ii) In the given potentiometer circuit AB is a uniform wire of length of 1 m and resistance 10?. Calculate the gradient along the wire along with the balance length AO (=I). (Delhi 2017)
Ans. (i)
(a) The basic principle of a potentiometer is that when a constant current flows through a wire of uniform cross sectional area and composition, the potential drop across any length of the wire is in direct proportion to that length.
v ∞ I
The comparison of emf of two cells- All the ends of potentiometer are connected to a battery Bx, key K and rheostat Rh in a way that the positive terminal of battery B is attached to the end A of the wire which completes the primary circuit.
Now, the positive terminals of the cells C1 and C2 are connected to A and the negative terminals to the jockey J through a two way key and a galvanometer and this is the secondary circuit.
Method-
(i) By closing key K, a potential difference is formed and rheostat is so adjusted that when jockey J’ is made to touch the ends A and B of wire, the deflection in the galvanometer is on both sides. Considering that in this position, the potential gradient is k.
(ii) Now plug is inserted between the terminals 1 and 3 so that the cell C1 is involved in the secondary circuit and jockey J slides on the wire at P1 to obtain the null point. The distance of P1 from A is measured as, AP1= l1
ε 1 = kl 1... (i)
(iii) Now plug is taken off between the terminals 1 and 3 and inserted between the terminals 2 and 3 in order to bring cell C2 in the circuit. Jockey is slided on wire and the null deflection position P2 is noted. Assuming the distance of P2 from A is l2, that is AP2 = Z2.
The emf of cell C2, e2 = kl2 …(ii)
... (iii)
Therefore, the emfs of the cells can be compared where if one is a standard cell, then the emf of the other cell will be calculated.
(b) The causes of one sided deflection-
(i) Potential difference between the ends of potentiometer wire is less than the emf of the cell in the secondary circuit.
(ii) The positive side of the driving cell is connected to the negative terminal of the cell in the secondary circuit.
(ii) 
Ques 9. If the temperature of a good conductor decreases, how does the relaxation time of electrons in the conductor change? (2 Marks)
Ans. We know: \(\rho = \frac{m}{ne^2 \pi}\)
When the temperature decreases, collision decreases, and thus relaxation time increases which in turn decreases the resistivity.
Ques 10. Name any one material having a small value of temperature coefficient of resistance. Write one use of this material. (1 Mark)
Ans. Nichrome, an alloy has a small value of temperature coefficient of resistance. It is used for making standard resistance coils.
Ques 11. Two wires A and B are of the same metal and of the same length and have their areas of the cross-section in the ratio of 2:1 if the same potential difference is applied across each wire in turn, what will be the ratio of current flowing in A & B? (2 Marks)
Ans. Since R = \(\frac{1}{A}\)
If the area is in the ratio 2:1 resistance will be in the ratio 1:2.
And I = \(\frac{V}{R} \implies I = \frac{1}{R}\)
Thus, the current will be in the ratio of 2:1
Ques 12. The plot of the variation of potential difference across a combination of three identical cells in series, versus current is shown in the figure. What is the emf of each cell? (Delhi 2008) (2 Marks)
Ans. Total emf of three cells in series = P.D corresponding to zero current = 6V
Thus, emf of each cell = \(\frac{6}{3}\) = 2V
Ques 13. Two wires of equal length, one of copper and the other of manganin have the same resistance. Which wire is thicker? (All India 2012) (3 Marks)
Ans. 
For both wires R and l are the same and ρ copper < p manganin.
∴ A copper < A manganin
i.e. Manganin wire is thicker than copper wire.
Ques 14. A cell of emf ‘E’ and internal resistance ‘r’ draws a current ‘I’. Write the relation between terminal voltage ‘V’ in terms of E, I and r. (Delhi 2013) (1 Mark)
Ans. V = E – I
Ques 15. Why is the terminal voltage of a cell less than its emf? (Comptt. All India 2013) (1 Mark)
Ans. The terminal voltage of a cell is less than emf because some current, however small, may be drawn to measure terminal voltage due to the internal resistance of the cell.
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