Assertion (A): The equivalent resistance ...

CBSE Class 12 Physics 2023 All Sets Paper

Question : 17 of 18

Marks: +1, -0

Assertion (A): The equivalent resistance between points A and B in the given network is 2R.

Reason (R): All the resistors are connected in parallel

Both Assertion (A) and Reason (R) are true and (R) is the correct explanation of (A).
Both Assertion (A) and Reason (R) are true and (R) is NOT the correct explanation of (A).
Assertion (A) is true and Reason (R) is false.
Assertion (A) is false and Reason (R) is also false.

Solution:

\frac{1}{R_1} = \frac{1}{2} + \frac{1}{2} \;\;\;\; \frac{1}{R_2} = \frac{1}{2} + \frac{1}{2}

\frac{1}{R} = \frac{2}{2} \;\;\;\; \frac{1}{R_2} = \frac{2}{2}

\frac{1}{R} = \frac{1}{1} \;\;\;\; \frac{1}{R_2} = 1

R_1 = 1\Omega

\;\;\;\; R_2 = 1\Omega

Then

R = R_1 + R_2

R = 1 + 1

R = 2Ω

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