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The physical occurrence with the presence and the flow of electric charge is called Electricity. To understand how electricity is formed it happens when electrons are loosely packed by the nucleus, they move easily within the body. They are known to be negatively charged particles hence when they make several charges then this movement is referred to as electric current or electricity.
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Keyterms: Electricity, electrons, nucleus, particles, electric current, Coulomb, Resistivity, potential difference
Read more: Electromagnetic Field
Electricity Formulas
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Before stepping to the formulas of electricity, below is the glossary of terminologies and definitions related to electricity.
- Potential Difference - When there is a need to move the electric charge between two chosen points, then the work done by doing so is called Potential Difference. In simpler terms, it is defined as the work done to move one charge from one to another point. I.e V ( S.I Unit of Potential Difference) = W (from one to another point). Thus we can define that 1 volt or 1v = 1J (Joule) or 1 Coulomb. So Potential Difference is called 1 volt when 1J of work is done by moving a charge from one to the other point. A voltmeter is equipment that is used to measure its magnitude. Moreover, the connection is parallel due to its high resistivity and potential difference remains constant.
- Power- It is defined as the rate of doing work, in other words, it is the work done in unit time. The Standard Unit of Power is Watt (W) which stands for joules per second.
- Charge - To define an electric charge it is a property of matter that leads it to experience a force when it is placed in an electromagnetic field. It consists of two charges positive and negative charges where like charges repel and unlike charges attract.
- Work or Energy - Work in physics is defined as the measure of energy transfer that happens when an object is moved due to an external force in the direction of the displacement
- Resistance - It is the property of the conductor where it restrains the flow of current through it. The resistor is the part in the circuit that resists the flow of current. To provide variable resistance a device named rheostat is used for the same.
- Electric Current - It refers to the amount of charge passing through a certain area in unit time. Electric Current is the continuous movement of the negatively charged particles, called electrons. They travel from negative terminal to positive terminal in a battery.
- Resistivity - it is the electrical resistance of a conductor of unit cross-sectional area and unit length. Resistance is directly proportional to the extent to which the conductor lies and is inversely proportional to the cross-sectional area of the conductor.
- Electromotive Force - the electromotive force refers to the electric potential which is given rise to by either electrochemical or by changing the magnetic field. The S.I unit for Electromotive force is joule per coulomb.
- Ohm’s Law - It is defined as the relation that exists between the potential difference applied to the ends of the conductor and current flowing through the conductor. In clear terms, if the physical state of the conductor remains unchanged then the current flowing through the conductor is always directly proportional to the potential difference across the two ends of the conductor.
- Conductors - Substances through which electric charges flow easily are called conductors. Conductors are known to have more free electrons loosely packed by nuclei of their atoms.
- Insulators - Substances through which electric charges don’t flow easily are called insulators. Insulators don’t have free electrons and are tightly packed by nuclei of their atoms.
- Equivalent Resistance - Equivalent Resistance is where aggregate resistance connected either in parallel or in series is calculated.
- Law of Combination Resistance in Parallel - The law of combination resistance in parallel states that the reciprocal of the combined resistance of all the resistors connected in parallel is equal to the sum of the reciprocal of all individual resistance.
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| Related Articles | ||
|---|---|---|
| Ohm's Law | Resistance | Resistors in Series |
Symbols and S.I Units present in the chapter Electricity
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| Physical Quantity | Symbols | SI Unit |
|---|---|---|
| Voltage | V | Volt (V) |
| Power | P | Watt (W) |
| Charge | Q | Coulomb (C) |
| Work energy | W | Joule (J) |
| Resistance | R | Ohm (Ω) |
| Current | I | Ampere (A) |
| Resistivity | ρ | Ohm metre ( Ω m) |
Important formulas on Electricity
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Current - The rate of flow of charges (Q) through a conductor is called and is given by,
Current - Charge/Time or t = Q/t where the S.I unit of current is ampere (A)
1 Ampere = 1 coulomb/1 Second
Some Other Important Formulas
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- Series Combination - A circuit is connected in series when an equal amount of current travels through the resistors. In such circuits, the voltage around each resistor is different. In a series connection, if any resistor is found to have technical issues, then the entire circuit is turned off.
It is calculated as: RTotal = R1 + R2 + ….. + Rn
- Parallel Combination - A circuit is said to be connected in parallel when the voltage is equal across the resistors. In such circuits, the current is diffused and again combines when branches meet at a common point.
It is calculated as: 1/RTotal = 1/R1 + 1/R2………..1/R(n)
For Equal Resistances
Rs = nR (For series connection)
Rp = R/n (For parallel connection)
Rs/ Rp = n2
Rs = Effective Resistance in series
Rp = Effective Resistance in parallel
- Power (P) = Work(W)/Time(T) = Energy Consumed/Time
- Power = Potential Difference x Current x time ; W = V x I x t ( W = I2 RT) = ( W = V2t/ R)
- Power = Potential Difference x Current ; P = W x T
- Power = (current)2 x Resistance ; P = I2 x R
- Power = (Potential Difference)2./Resistance ; P = V2/R
- Electric Energy = Power x time; Electric energy = P x t
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Sample Questions
Ques. An electrical lamp gleams for exactly 4 hours and fetches a current of 0.5 A. Determine the amount of charge flowing through the lamp. (3 Marks)
Ans. Current I = 0.5 A
Time taken t = 4 hours
t= 4 × 3600 = 14400 s,
Charge Q = I × t
= 0.5 ×14400
Q= 7200 C
Ques. An electrical lamp gleams for exactly 8 hours a day. It fetches the current of 1 A. Determine the amount of charge traveling through the lamp. (5 Marks)
Ans. Current, I = 1 A
Time taken, t = 8 hours
Time taken = 8×3600
Time taken = 28800 s,
Now, quantity of Charge,
Q=I×t
Q=1×28800
Q = 28800 C
Potential Difference - The potential difference between two ends in a circuit is described as the work done to move electric charge from different points in an electric circuit.
To calculate Potential Difference -
Potential Difference = Work Done/Charge or V = W/Q
Ques. Calculate the work done to carry a charge of 3 C if the potential difference between two points is 10 V. (4 Marks)
Ans. It is given that charge, = 3C
Potential Difference between two ends = 10V
Work Done (W) = ?
V = W/Q
So, W = V x Q
W = 10V x 3C = 30J
Ques. 5000 J of work would be done to carry how much charge between two points having a potential difference of 100 V? (4 Marks)
Ans. It is given that, potential difference = 100V
Work Done (W) = 5000 J
Charge (Q) = ?
Since V = W/Q
Q = W/V
Q = 5000 J / 100V = 50C
Ohm's law = Potential Difference across the two points of a conductor is directly proportional to the current flowing through the circuit where the temperature is constant.
It is represented mathematically as -
V ∝ I or V=IR , I = VR & R = V/I
Where R is constant resistance for any given metal.
The value of resistance depends upon the nature and physical dimensions of a particular conductor.
Ques. An electric circuit has a 24 V battery and a resistor of 60 ohms. What will be the current in the circuit? The resistance of the connecting wire is negligible. (3 Marks)
Ans. Given that, Potential Difference (V) = 24V
And Resistance = 60 ohm
Current (I) = ?
Since R = V/I then, I = V/R
I = V/R
I = 24V/60Ω = 0.4A
Ques. If the potential difference between the ends of an electric motor is 220 V and an electric current of 5 A is traveling through it, what will be the resistance of the electric motor? (5 Marks)
Ans. Given, electric current (I) = 5 A
Potential difference (V) = 220 V
Resistance (R) =?
Since R = V/I
So R = 220V/5A = 44Ω
Coulomb’s law = it states that force of attraction or repulsion between two stationary point charges is directly proportional to the product of the magnitude of the two charges and inversely proportional to the square of the distance between them.
To understand it clearly
The figure depicts two charges q1 and q2 and these two charges are separated by a distance r. Then according to coulomb's law, it states that the force of attraction or repulsion between them is - F ∝ q1q2 or F ∝ 1/(r)2
Therefore
F ∝ q1q2/(r)2
Or
F = k q1q2/(r)2
Where k is the constant of proportionality. The value of k depends on the factors such as the nature of the medium between two charges.
Electric Power - It is referred to as the rate at which energy is consumed in an electrical circuit.
Power = Voltage x Current
Derivation of Power Formula-
We are aware that, Potential Difference = Work Done/Charge
V = W/Q
Also, W = V x Q …..(I)
Now,
Power = Work done/Time Taken
P = W/T
Putting W = VQ
P = V(Q/T)
Thus, P = V x I
Ques. An electric heater carries a potential difference of 220 V and resistance is 70 Ω. Determine the magnitude of the current traveling through the heater. (3 Marks)
Ans. It is Given that :
Resistance R = 70 Ω
Voltage V = 220 V
Using Current Formula:
I = V / R
= 220 / 70
I = 3.1428 A
Ques. An electrical lamp gleams for exactly 4 hours and fetches out a current of 0.5 A. Determine the amount of charge traveling through the lamp. (3 Marks)
Ans. Current I = 0.5 A
Time taken t = 4 hours
t= 4 × 3600 = 14400 s,
Q = I × t
= 0.5 ×14400
Q= 7200 C
Resistivity - It is the flow of current from one end to the other in a material
It is calculated as
ρ = RA/l.
Where ρ stands for the resistivity, R is the resistance, l is the length of the material and A is the area of cross-section.
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