Consider a simple circuit shown in fig
stands for a variable resistance R'. R' can vary from R0 to infinity. r is internal resistance of the battery $(r << R << R_{0})$
a) Potential drop across AB is nearly constant as R' is varied.
b) Current through R' is nearly a constant as R' is varied.
c) Current I depends sensitively on R'
d) $I \geq \frac{V}{r + R} always$

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a & d are true

a, b & c are true

All are true

b & d are true

answer is A.

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Detailed Solution

Since, R and R' are in parallel, potential difference across them is same. Effective resistance would be

$R_{eff} = \frac{RR'}{R + R'} = \frac{R}{\frac{R}{R'} + 1} = R$ , since R << R0 which is the minimum value of R'.

So potential drop across AB will be nearly IR most of the time.

Also, Current I is $I = \frac{V}{R_{eff} + r} \geq \frac{V}{R + r} (∵ R_{eff} might slightly be less than R)$ .

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