Question

A battery has an emf of $ 15\, V $ and internal resistance of $ 1 \Omega $ . Is the terminal to terminal potential difference less than, equal to or greater than $ 15\, V $ if the current in the battery is $ (1) $ from negative to positive terminal, $ (2) $ from positive to negative terminal $ (3) $ zero current ?

• A. Less, greater, equal
• B. Less, less, equal
• C. Greater, greater, equal
• D. Greater, less, equal

Answer 1

Answer: (D)

If $E$ is the emf of the battery, $r$ the internal resistance, $i$ the current drawn and $V$ the $PD$ across the plates of battery, then
$ V = E -ir$
Case I : When the direction of current in the battery is from $−ve$ to $+ ve$ or outside $+ ve$ to $−ve$, then
$ i = + ve$ (during discharging)
$V = E + ir$
Case II : When the direction of current in the battery is from $+ ve$ to $−ve$ or outside $−ve$ to $+ve$, then
$ i = − ve$ (during charging)
$V = E + ir$
$⇒ V > E $
Case III : When zero current, then
$ i = 0$
$V = E $