Answer to Question #184579 in Electric Circuits for Niall Rio

Question

When the switch is open, the potential difference across the terminals of a battery is 200 V. When a current of 2.0 A flows, the potential difference across the battery drops to 16 V. (a) If this battery consists of two identical cells in series, what is the electromotive force of each cell? (b) If this battery consists of two identical cells in series, what is the internal resistance of each cell? (c) If this battery consists of two identical cells in parallel, what is the electromotive force of each cell? (d) If this battery consists of two identical cells in parallel, what is the internal resistance of each cell?

Answer 1

(a) when cells are connected in series,

emf of battery = 200 V

emf of single cell(E) = 100 V

(b) $2E-2Ir=16$

$r=\dfrac{2E-16}{2I}=\dfrac{(2\times100)-16}{2\times2}$

$r=46\space \Omega$

(c) when cells are connected in parallel,

emf of single cell(E) = 200 V

(d) equivalent resistance when two resistances are connected in parallel,

$r_{eq}=\dfrac{r}{2}$

$E-Ir_{eq}=16$

$E-I\times\dfrac{r}{2}=16$

$r=\dfrac{2(E-16)}{I}=\dfrac{2(200-16)}{2}$

$r=184\space\Omega$