Question

The given figure shows a circuit diagram containing 12 cells, each of EMF 1.5 V and internal resistance $0.25\Omega$. Calculate the:

(a) total internal resistance.
(b) total EMF.
(c) reading shown by the ammeter.
(d) Current in $12\Omega$ and $8\Omega$ resistors.
[5 MARKS]

Answer 1

part a,b,c: Each 1 Mark

part d: 2 Marks

(a) Total internal resistance of 12 cells in series, r = 12 $\times$ 0.25 = $3\Omega$
(b) Total EMF = 12 $\times$ 1.5 = 18 V
(c) Reading shown by ammeter,

I = V/R ,therefore we will have to calculate total resistance in circuit.

We have already calculated total internal resistance. Now we will calculate total external resistance(R).

R = Resistance of ammeter + resistance of X + resistance of parallel circuit

Resistance of parallel circuit

12 ohms and 12 ohms are in parallel , therefore

$\frac{1}{R_{eq}}=\frac{1}{12}+\frac{1}{12}=\frac{2}{12}$

$R_{eq}=6ohms$

R = Resistance of ammeter + resistance of X + resistance of parallel circuit

R = 0.8 + 2.2 + 6 = 9 ohms

Total resistance of circuit = total internal resistance + total external resistance = R+r

$I=\frac{ϵ}{R+r}=\frac{18}{9+3}=\frac{18}{12}=1.5A$

(d) Potential difference across parallel circuit,
$V=IR=1.5\times 6=9V$
[$\because$ Equivalent resistance of $4\Omega$, $8\Omega$ and $12\Omega$ = $6\Omega$]
Current in $12\Omega$ resistor,
$I=\frac{V}{R}=\frac{9}{12}=0.75A$
Current in $8\Omega$ resistor, $I=\frac{V}{R}=\frac{9}{8+4}=0.75A$