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Q.

The expression for the equivalent resistance of the combination of resistors $R_{1}, R_{2} and R_{3}$ in a parallel combination is

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a

R_{s} = R_{1} + R_{2} + R_{3}

b

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

c

Both 1 and 2

d

None of the above

answer is B.

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Detailed Solution

Given the resistors

R 1, R 2 and R 3

are connected in parallel with a battery, key and an ammeter connected. The current I flows through the circuit. Let the voltage (potential difference) across each resistance be V. We know the voltage remains the same for a parallel combination.
Using Ohm's law we have

V = I_{1} R_{1}; V = I_{2} R_{2} and V = I_{3} R_{3}

I_{1} = \frac{V}{R_{1}}; I_{2} = \frac{V}{R_{2}} and I_{3} = \frac{V}{R_{3}}

Total current in the circuit

I_{p} = I_{1} + I_{2} + I_{3}

\frac{V}{R_{p}} = \frac{V}{R_{1}} + \frac{V}{R_{2}} + \frac{V}{R_{3}}

Therefore

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}}

Here in parallel combination of resistors, the reciprocal of equivalent resistance is equal to the sum of the reciprocals individual resistances.

https://lh6.googleusercontent.com/QJ-ad9aFDgAWznjRU7l1Vqx-y7swoY43eTZzZxpwt4jILa4d0z1wf13VdN1k8L7AuAFL7j0h9wfw_Doc2bSNsaO1RpwHc1xbLo1tUjPKfLduQDkyDn3yC3z0L3yDx4_-HxuANKq8PL-Lg9OedFEEOF_aT2J5_LgBlX-I7D955QKvO0OgBf1-khMRFBpzzawEt0Tfww

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