A battery of e.m.f. E has an internal resistance 'r'. A variable resistance R is connected to the terminals of the battery. A current I is drawn from the battery. V is the terminal P.D. If R alone is gradually reduced to zero, which of the following best describes I and V?

Question

A battery of e.m.f. E has an internal resistance 'r'. A variable resistance R is connected to the terminals of the battery. A current I is drawn from the battery. V is the terminal P.D. If R alone is gradually reduced to zero, which of the following best describes I and V? (A) I approaches E /r, V approaches E (B) I approaches infinity, V approaches E (C) I approaches zero, V approaches E (D) I approaches E /r, V approaches zero

Tardigrade Admin · Accepted Answer

Current, i=(E/R+r) when R decreases to 0, i=(E/r) Similarly, potential difference V=i R when R decreases to 0, V=0

$I$ approaches $E / r, V$ approaches $E$

$I$ approaches infinity, $V$ approaches $E$

$I$ approaches zero, $V$ approaches $E$

$I$ approaches $E / r, V$ approaches zero

Current, $i = \frac{E}{R + r}$ when $R$ decreases to $0, i = \frac{E}{r}$
Similarly, potential difference $V = i R$ when $R$ decreases to $0, V = 0$

Q. A battery of e.m.f. E has an internal resistance ′r′. A variable resistance R is connected to the terminals of the battery. A current I is drawn from the battery. V is the terminal P.D. If R alone is gradually reduced to zero, which of the following best describes I and V?

I approaches E/r,V approaches E

I approaches infinity, V approaches E

I approaches zero, V approaches E

I approaches E/r,V approaches zero

Current, i=R+rE​ when R decreases to 0,i=rE​ Similarly, potential difference V=iR when R decreases to 0,V=0

$I$ approaches $E / r, V$ approaches $E$

$I$ approaches infinity, $V$ approaches $E$

$I$ approaches zero, $V$ approaches $E$

$I$ approaches $E / r, V$ approaches zero

Current, $i = \frac{E}{R + r}$ when $R$ decreases to $0, i = \frac{E}{r}$
Similarly, potential difference $V = i R$ when $R$ decreases to $0, V = 0$