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One of the simplest combinations of resistors are series and parallel connections. Resistors can be connected in both parallel and series in the same circuit across different loops to produce a more complex resistive network. Resistors is an important part of electric circuits on whose functionality the regualtion of the current level of a device depends.
Read More: Electrostatics Potential and Capacitance Important Question
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Key Terms: Resistance, electricity, Series and parallel resistors, circuits, reistors in parallel, resistors in series.
What is Resistors?
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Resistors are two-terminal devices. Therefore, the functionality of a resistor are voltage division, regulation of current in the device and adjusting signal level. Representation of a resistor is done through Ohm’s Law. The SI unit of resistance is the ohm. It is denoted in the form of a Greek letter, i.e “Ω”. A resistor is used in an electrical circuit for protection, operation, current control, etc.
Many types of resistors are available. Some of them are:
- Wire-wound resistor.
- Semi-conductor resistor.
- Flim resistor.
- Carbon Composition resistor.
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Current Electricity Detailed Video Explanation:
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Types of Resistors
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A resistor works by converting the electrical energy into heat, which is expelled into the air. There are many types of resistors used in the industry. A few of them are listed below:
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Light-dependent resistor or LDR
The resistance of this kind of resistor depends on the intensity of light falling on it . This resistor works on the principle of photoconductivity. When an LDR is kept in the dark place its resistance is high and when the LDR is kept in the light its resistance will decrease.
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Variable resistor
This one is the most commonly used type of resistor; these resistors consist of a fixed value of resistance between two terminals. Different types of variable resistors are rheostats, digital resistors, and potentiometers.
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Film type resistor or Cermet Resistor
Under these three types of resistors come such as carbon, metal, and metal oxide.
These resistors are made with the deposition of pure metals. The resistance value of a resistor can be changed or controlled by increasing the width of the deposited film.
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Ohmic resistors
These are the types of resistors that follow ohm’s law. These resistors are called the ohmic resistors or linear resistors.
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Carbon resistor
It is one of the most common types of resistors used in electronics carbon resistors that come in different physical sizes. These resistors are mostly preferred because they are very cheap, solid, and can be inserted directly onto the circuit boards.
Read More: Types of Motors
Combination of Resistors
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Resistors are basically two-terminal devices. That is why the functions of a resistor are the division of voltage and the regulation of current in the device.
Mathematical representation of resistors is done by applying ohm’s law. According to Ohm’s Law:
\(R = \frac{V}{I}\)
A series circuit includes a path along which the whole current flows through each component.
On the other hand, A parallel circuit comprises different paths so that the current divides and only part of the current flow through any path.
If you take an example of our home electrical circuit, the voltage applied across each light or bulb or any other appliance is the same, but each of these loads extracts a different amount of current according to its power requirements. This is achieved through parallel connections.
Now let us understand the combination of resistances with series and parallel in detail.
Read More: DC Generators, Types of DC Motors
Resistors in Series
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A Series combination is a combination when two or more resistors are connected one after the other (As shown in the figure). In series combination current through each resistor is constant and there is only one path for the flow of electric current. In a series combination, the potential difference across each resistor is different depending upon the value of resistance.
Series Combination
Here, in this case as it’s visible that the current passes through all the three resistances . So, the equivalent resistance of circuit is equal to the sum of individual resistances.
| Re = R1 + R2 + R3 + ........Rn |
Advantages:
- It is used when not one but hundreds of bulbs or lights are to be used together.
- It is safer because less current flows through the circuit
- It’s easier to switch on or off all the bulbs or lights or all the appliances as they are connected together
Disadvantages:
- One single appliance cannot be switched off separately as all the electrical appliances have only one switch
- If one component is fused or stops working then the other component of circuit will not function.
- All the components do not get the same voltage as the voltage gets divided in series or combinations.
Read More: Unit of Conductivity
| Ques. A resistor with an electrical resistance value of 100 ohms, is connected to another resistor with a resistance value of 200 ohms. The two resistances are connected in series. Find the total resistance across the system? Ans. Here, R1 = 100 Ω and R2= 200 Ω Rtotal = 100 + 200 = 300 Ω |
Resistors in Parallel
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If these are more than one path for the flow of current in a circuit (As shown in the figure) then the combination of resistances is called parallel combination. Potential across each resistance is same and equal to applied potential. Current through each resistor is constant. The parallel combination is used in homes for different household appliances each appliance has a separate switch which can be turned on or off as required.
| I= I1 +I2 +I3 V= (1/R1 + 1/R2 + 1/R3 ) |
In parallel combinations of resistors, if one component of circuit or resistor is damaged then rest of the component of the circuit will perform their work smoothly without any hindrance. It is because of the presence of more than one path for the flow of electric current.
Parallel Combination
Advantages:
- Individual appliance can be turned on or off separately
- Each electrical appliance gets the same voltage as the power supply line.
- If for some reason one electrical appliance stops working due to some defect then all other appliances won’t stop working.
Disadvantages:
- It is less safe as more current can pass through the circuit
- This method is tedious to use if thousands of appliances or bulbs are to be switched on or off together.
Let us understand this through one example : If the two light bulbs were connected in parallel, they would be equally as bright as if they were connected separately to the battery . But in this case the battery would die soon since it is supplying its full energy to both light bulbs . In case of series combination, the battery would last just as long as it would with a single light bulb ,only the brightness will be divided amongst the bulbs.
There is one more type of circuit i.e. combination circuit.
The combination circuit contains multiple resistors that are connected in combination with both the series and parallel connections.
In this type of circuit the circuit can be broken up into a series component and a parallel component. Simple circuits can be solved using the formulae stated above, but advanced circuits involve more mathematical treatment. Such type of resitances are solved by using advanced laws such as kirkchoff’s laws.
The presentation below highlights the main points discussed in this article.
Read more:
| Chapter Related Topics | ||
|---|---|---|
| Electrical Current | Circuit Diagram | Drift Velocity |
| Resistor Colour Codes | Ampere | Unit of current |
| Unit of voltage | Current density | Unit of specific resistance |
Things to Remember
- Resistors are two-terminal devices, and the functionality of a resistor are voltage division, regulation of current in the device and adjusting signal level.
- Representation of a resistor is done through Ohm’s Law.
- The SI unit of resistence is the ohm. It is denoted in the form of a Greek letter, i.e “Ω”.
- In reisstors in series connection, resistors are in a sequential array of resistors to form an electronic device.
- In resistors in parallel connection, the terminals of resistors are connected to the same terminal of the other resistor to form an electronic device.
Previous Year Questions
- If now we hav.e to change the null point at 9th 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 4Ω 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 ]
- When two resistances R1 and R2 are connected in series, they consume 12W power….[KEAM]
- Nichrome is used as electrical heating element because of its…[KEAM]
- In the figure shown below, the terminal voltage across E2 is…[KEAM]
- In a potentiometer of wire length ll, a cell of emf V is balanced at a...[KEAM]
- A potentiometer wire AB having length L and resistance 12r is joined to… [JEE Main 2019]
- A resistance is shown in the figure. Its value and tolerance are given respectively by ...[JEE Main 2019]
- The resistance between any two vertices of the triangle is...[JEE Main 2019]
- In the given circuit the cells have zero internal resistance. The currents...[JEE Main 2019]
- In The Given Circuit Diagram…...[JEE Main 2019]
- In the given circuit, an ideal voltmeter connected across the 10Ω resistance...[JEE Main 2019]
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Sample Questions
Ques. Is it preferable to connect bulbs in series or in parallel? a) Series b) Parallel c) Both series and parallel d) Neither series nor parallel (2 marks)
Ans. Correct answer is option b.
Explanation: Bulbs are connected in parallel so that even if one of the bulbs blow out, the others continue to get a current supply.
Ques. Calculate the total resistance between the points A and B.
Ans. Correct answer is option c.
Explanation: 1 ohm in parallel with 2 ohm give 2/3 ohm equivalent which is in series with 4 ohm and 3 ohm so total resistance between A and B = 4 + 2/3 + 3 = 23/3 = 7.67 ohm.
Ques. State the the two Kirkchoff’s laws. Briefly explain how these laws are justified.
The current is drawn from a cell of emf E and internal resistance r connected to the network of resistors each of resistance r as shown in the figure. Obtain the expression for (i) the current drawn from the cell and (ii) the power consumed in the network. (CBSE Delhi 2017)(5 Marks)
Ans.
- The Kirchoff's laws are as follows:
Kirchhoff’s junction rule, also known as Kirchhoff’s point rule, states that the algebraic sum of currents in a network of conductors meeting at a point is zero. In simple words, the law can be restated that the sum of currents entering a junction equals the sum of currents leaving that junction. The law is diagrammatically explained in the figures drawn below.
- In figure A, the sum is i1 + i2 = i3.
- In figure B, i1 = i2 + i3 + i4.
- In figure C, i1 + i2 + i3 = 0.
The second law, known as Kirchhoff’s loop rule or Kirchhoff’s voltage law, states that the sum of electromotive forces in a loop equals the sum of potential drops in the loop. Alternatively, it could be stated that the directed sum of voltages around any closed loop is zero. In simple words, the sum of potential differences across all components in a closed loop is zero. This is well illustrated in the diagram below.
In the circuit in the diagram, the potential difference Vb - Va is represented as E1. That is to say Vb - Va = E1.
The Kirkchoff’s laws are justified as they are in coherence with the law of conservation of energy and conservation of charge.
- The circuit diagram can be simplified as follows:
Hence, the equivalent resistances can be calculated using the current in series and parallel formulae. Here, r,r,2r and 2r between A and B are in parallel. Hence, equivalent resistance is :
Ques. In the two electric circuits shown in the figure, determine the readings of the ideal ammeter (A) and the ideal voltmeter (V). (Delhi 2015 C , 3 Marks)
Ans. In First Circuit,
Reading of ideal voltmeter = 6 V
Net potential difference = 9 + 6 = 15 V
Total resistance = 1 + 1 = 2 Ω
Current in ammeter = V/R = 15/2 = 7.5 A
In Second Circuit,
Reading of ideal volt meter = 6 V
Net potential difference = 9 – 6 = 3 V
Total resistance = 1 + 1 = 2 Ω
Current in ammeter = V/R = 3/2 = 1.5 A
Ques. A 100 V battery is connected to the electric network as shown. If the power consumed in the 2 Ω resistor is 200 W, determine the power dissipated in the 5 W resistor. (CBSE foreign 2014, 5 marks)
Ans. The circuit can be reduced to the one given below :
The current which is drawn from the battery is I2 = P/R = 200/2 = 100. Hence, I = 10 A for the 2 Ω resistor.
Current drawn from AB branch = (40x10)/(40+10) A = 8 A
Hence, the required power P = I2R = 64x5 = 320 W
Ques. Calculate the current through each resistor in the figure given below. (CBSE Delhi 2015 C)(3 marks)
Ans.
Ques. Calculate the value of resistance R in the circuit given below so that the current in the circuit is 0.2 A. What is the potential difference between the points A and B? (3 marks)(CBSE AI 2012)
Ans.
Ques. A wire of resistance 8R is bent in the form of a circle. What is the effective resistance between the ends of a diameter AB? (CBSE Delhi 2010)(1 mark)
Ans. As shown in the figure, the wire is now equivalent to 2 resistances connected in parallel. Resistance of each semi circular portion is 4R. Hence , the equivalent resistance will be: 1/R = (¼ + ¼ ) = ½ . So R = 2 Ω.
Ques. Given the resistances of 1 Ω, 2 Ω, 3 Ω, how will you obtain an equivalent resistance of: (a)11/3 Ω , (b) 11/5 Ω? (CBSE foreign 2015)(2 marks)
Ans. (a) The figure below leads to an equivalent resistance of 11/3 Ω.
This is because equivalent resistance in series is 11 Ω . Since 3 such rows are there, overall the resistance becomes 11/3 Ω
(b) For 11/5 Ω, 5 rows of 1 Ω , two 2 Ω resistors and two 3 Ω resistors connected in series (Similar to the one above, but 5 rows instead of 3) will lead to a resistance of 11/5 Ω
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