Resistors In Parallel Formula: Definition And Features

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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.

Table of Content

What Is Resistors In The Parallel?
Formula Of Resistors In Parallel
Features Of Resistors In Parallel
Things to Remember
Previous Year Questions
Sample Questions

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

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.

Discover about the Chapter video:

Current Electricity Detailed Video Explanation:

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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.

R_Total = R₁ + R₂ + R₃………. + R_n

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

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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.

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/R_p =(1/4) +(1/6)+(1/2)

1/R_p =11/12

R_p=12/11

R_p = 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

R_eq

= 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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Resistors In Parallel Formula: Definition And Features

What Is Resistors In The Parallel?

Current Electricity Detailed Video Explanation:

Formula Of Resistors In Parallel

Features Of Resistors In Parallel

Things To Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

2.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

3.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

4.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

5.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

6.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

Similar Physics Concepts

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Resistors In Parallel Formula: Definition And Features

What Is Resistors In The Parallel?

Current Electricity Detailed Video Explanation:

Formula Of Resistors In Parallel

Features Of Resistors In Parallel

Things To Remember

Previous Year Questions

Sample Questions

CBSE CLASS XII Related Questions

2. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

3.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

4.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

5.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

6.Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

2.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

3.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

4.
What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

5.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

6.
Two thin lenses of focal length \( f_1 \) and \( f_2 \) are placed in contact with each other coaxially. Prove that the focal length \( f \) of the combination is given by \[ f = \frac{f_1 f_2}{f_1 + f_2}. \]