Question

Study the circuit diagram shown below carefully and calculate the:
(a) current in the main circuit.
(b) current in each of the resistors in the parallel circuit.

[5 MARKS]

Answer 1

Each subpart: 2.5 Marks

(a) Equivalent resistance of $1.5\Omega$ and $3\Omega$ in parallel,
$\frac{1}{R_1}=\frac{1}{1.5}+\frac{1}{3}=\frac{2+1}{3}=\frac{3}{3}=1\Omega$
or $R_1=1\Omega$
Equivalent resistance of $6\Omega$ and $12\Omega$ in parallel,
$\frac{1}{R_2}=\frac{1}{6}+\frac{1}{12}=\frac{2+1}{12}=\frac{3}{12}=\frac{1}{4}$
or $R_2=4\Omega$
Now, the total equivalent resistance of circuit, $R=R_1+R_2=1+4=5\Omega$
$\therefore$ Current in main circuit, $I=\frac{V}{R}=\frac{9}{5}=1.80A$
(b) Potential difference across $1.5\Omega$ and $3\Omega$ , $V_1=IR=1.8\times 1=1.8V$
$\therefore$ Current in $1.5\Omega$ resistor,
$I_1=\frac{V_1}{R}=\frac{1.8}{1.5}=1.2A$
Current in $3\Omega$ resistor,
$I_2=\frac{V_1}{R}=\frac{1.8}{3}=0.6A$
Now, potentiaal difference across $6\Omega$ and $12\Omega$, $V_2=1.8\times 4=7.2V$
Current in $6\Omega$ resistor,
$I_3=\frac{V_2}{R}=\frac{7.2}{6}=1.2A$
Current in $12\Omega$ resistor,
$I_4=\frac{V_2}{R}=\frac{7.2}{12}=0.6A$