Question

The given figure shows a battery having an EMF of 9V and internal resistance of $0.6\Omega$, connected to three resistors A, B and C. ?

(a) Calculate the combined resistance of B and C.
(b) Calculate the total resistance of A, B and C.
(c) Calculate the total resistance of the circuit.
(d) Calculate the current in each of the three resistors A, B and C.
[5 MARKS]

Answer 1

part a, b, c: Each 1 Mark
part d: 2 Marks

(a) The resistors B and C are in parallel. Let their equivalent resistance be R'. Then :
$\frac{1}{R^{\prime }}=\frac{1}{4}+\frac{1}{6}=\frac{3+2}{12}=\frac{5}{12}$
Or $R^{\prime }=\frac{12}{5}=2.4\Omega$
(b) Total resistance of A, B and C
$=2+2.4=4.4\Omega$
(c) Total resistance of circuit
$=4.4+0.6=5\Omega$
(d) Main current in the circuit,
$I=\frac{EMF}{Totalresistance}=\frac{9}{5}=1.8A$
$\therefore$ Current in resistor A is 1.8 A.
Potential difference across parallel circuit, $V=IR=1.8\times 2.4=4.32V$
$\therefore$ Current in resistor $B,I_1=\frac{V}{R}=\frac{4.32}{4}$
= 1.08 A
$\therefore$ Current in resistor $C,I_2=\frac{V}{R}=\frac{4.32}{6}$
= 0.72 A