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Resistors can be termed as the universal components in the electronic industry. In circuits analysis, the values of two or more resistors are required known, hence we use resistors in the parallel formula.
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Key Terms: Electric, Circuit, Resistance, Formula, Network, Current, Reciprocal, Components, Resistor, complex network
What Is Resistors In The Parallel?
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Resistors are either connected as a series or in a parallel pattern when both of their terminals are respectively connected to each terminal of the other resistor or resistors to create a more complex network.
Resistors In Parallel
The voltage across the resistors for each resistor in a parallel pattern will be the same whereas the current will be in proportion to the resistance of each individual resistor. When resistors are connected in parallel, then the supply current is equal to the sum of the currents through each resistor.
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Formula Of Resistors In Parallel
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To find the equivalent resistance of a number of resistors in parallel, the reciprocal of resistance i.e. 1/R is used. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each resistance.
\(\frac{1}{R_{Total}} =\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}.......\frac{1}{R_n}\)
The unit of resistance is the Ohm, which is equal to a Volt per Ampere. Larger resistors with kilo-Ohm or mega-Ohm resistances are common, as well.
RTotal = R1 + R2 + R3………. + Rn
Resistors In Series
Features Of Resistors In Parallel
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The major features of the resistors in parallel are:
- Parallel resistance is smaller than any individual resistance in the combination.
- Each parallel resistor has an equal amount of voltage of the source which is applied to it.
- Each of the parallel resistors does not get the full current hence they divide it.
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Things To Remember
- Resistors can be termed as the universal components in the electronic industry.
- The reciprocal of resistance i.e. 1/R is used.
- Parallel resistance is smaller than any individual resistance in the combination.
- Larger resistors with kilo-Ohm or mega-Ohm resistances are common.
- The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of each resistance.
Previous Year Questions
- A Circuit Contain Two Resistors R1 And R2 In Series…. [JIPMER 2019]
- Twelve Resistors Each Of Resistance 16 Are Connect… [BITSAT 2019]
- Three Resistors 1 2 And 3 Are Connected To Form A… [VITSAT 2012]
- Three Equal Resistors Connected In Series Across A…. [NEET 1998]
- A Set Of N Equal Resistors Of Value R Each Are Con… [NEET 2018]
- 13 Resistors Each Of Resistance R Are Connected In… [KCET 2003]
- Four Resistors Of 100 Each Are Connected In The Fo… [KCET 1996]
- Two Resistors Of Resistances 200 K And 1 M Respect… [KEAM]
- Four Resistors 100 Omega 200 Omega 300 Omega And 4…
- You Are Given N Resistors Each Of Resistance R The… [GUJCET 2006]
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- A Current Of 5a Is Passing Through A Metallic Wire… [VITEEE 2006]
- A 2 V Battery A 15 Resistor And A Potentiometer O… [JCECE 2011]
- Three Resistances Each Of 4 Are Connected To Form… [NEET 1993]
- Charge Passing Through A Conductor Of Cross Sectio… [VITEEE 2012]
Sample Questions
Ques 1. Define resistors in parallel. (2 Marks)
Ans. Resistors are either connected as a series or in a parallel pattern when both of their terminals are respectively connected to each terminal of the other resistor or resistors to create a more complex network.
The voltage across the resistors for each resistor in a parallel pattern will be the same whereas the current will be in proportion to the resistance of each individual resistor. When resistors are connected in parallel, then the supply current is equal to the sum of the currents through each resistor.
Ques 2. Calculate the resultant resistance of a parallel circuit containing three resistors; R1 = 4Ω, R2 = 6Ω and R3 = 2Ω. (2 Marks)
Ans. Given value of resistors are,
R1 = 4Ω,
R2 = 6Ω,
R3 = 2Ω
\(\frac{1}{R_{Total}} =\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}.......\frac{1}{R_n}\)
1/Rp =(1/4) +(1/6)+(1/2)
1/Rp =11/12
Rp=12/11
Rp = 1.0909 Ω
Ques 3. State three features of resistors in parallel. (2 Marks)
Ans. The major features of the resistors in parallel are:
- Parallel resistance is smaller than any individual resistance in the combination.
- Each parallel resistor has an equal amount of voltage of the source which is applied to it.
- Each of the parallel resistors does not get the full current hence they divide it.
Ques 4. What is the equivalent resistance of a 1000 kilo-ohm and a 250 kilo-ohm resistor connected in parallel? (2 Marks)
Ans. 1/ 1eq = 1/R1 + 1/R2
1/ 1eq = 1/1000 + 1/250
= 5/1000
Req
= 200 kilo−Ω
Ques 5. Mention a difference between the minimum and maximum effective resistance. (1 Mark)
Ans. Differences between the minimum and maximum effective resistance are:
Minimum effective resistance is the least possible resistance of the circuit whereas maximum effective resistance is the total possible resistance of the circuit
Ques 6. What is the series connection of resistors? (1 Mark)
Ans. The resistors are connected across the two points in the circuit in a structure that the current flowing through each resistor is the same and only one path is available for it to flow hence the resistors are said to be connected in series.
Ques 7. Is there any advantage of connecting electrical devices in parallel with the battery instead of connecting them in series? (1.5 Marks)
Ans. Yes, connecting electrical devices in parallel with the battery instead of connecting them in series has an advantage. A parallel circuit divides the current through electrical gadgets and total resistance in a parallel circuit is decreased. Therefore, it is helpful particularly when each gadget has different resistance and requires different current to operate properly.
Ques 8. Define electric resistivity material and do mention its SI Unit. (1.5 Marks)
Ans. The resistivity material is a resistance of a unit length of the conductor with the unit area of cross-section. SI Unit is ohm meter.
Ques 9. what is the reciprocal resistance used to evaluate the equivalent resistance of a number of resistors in parallel? (1 Mark)
Ans. To find the equivalent resistance of a number of resistors in parallel, the reciprocal of resistance i.e. 1/R is used.
Ques 10. What is a mixed combination of resistances? (1.5 Marks)
Ans. A mixed combination of resistance is a circuit including both series and parallel combinations.
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