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  • Consider a simple circuit shown in Figure variable resistance R’. R’ can vary from R_0 to infinity. r is internal resistance of the battery (r<<R<<R _0)

Consider a simple circuit shown in Figure.

 variable resistance R’. R’ can vary from R_0 to infinity. r is the 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\geqslant \frac{V}{r+R} always.

Answers (1)

The correct option is E (a) and (d) above
Here R and R’ are in parallel so the potential drops across both resistors will be the same and are nearly constant.

R_{eq} = \frac{RR^{'}}{R+R^{'}} + r

Current in the circuit, 

 I = \frac{V}{R_{eq}} = \frac{V}{\frac{RR^{'}}{R+R^{'}}+ r}

Since R<<R0⇒R<<R'

So, the equivalent resistance of R and R’ will be less than R,

Req≤R+r

The current flow in the circuit will be,

I = \frac{V}{R_{eq}}

I \geqslant \frac{V}{R+r} always
Potential drop across AB,

V_{AB} = I \times \frac{RR'}{R+R'}

= \frac{V}{\frac{RR'}{R+R'}+r} \times \frac{RR'}{R+R'}′

V_{AB} = \frac{V \times RR'}{r(R+R')} \ \ \\ \ \ \ \ \ \ \ = \frac{VR}{R+r}

Since potential across AB does not depend upon R', therefore potential across it almost remains constant.

Current through R',

I' = \frac{V_{AB}}{R'} = \frac{V \times R}{R'(R+r)}

Hence current through R' is not constant as R' is varied. Also, current I depend sensitively on R'.

Final Answer: (a), (d)

Posted by

infoexpert24

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