Question

A battery of EMF 3 V is connected in series with an ammeter, a $10\Omega$ coil of wire and with a parallel combination of resistances of $3\Omega$ and $6\Omega$. Draw a circuit diagram of the arrangement and calculate the:
(a) reading of the ammeter.
(b) the potential difference across $3\Omega$ resistor.
(c) current flowing through $3\Omega$ resistor.
[5 MARKS]

Answer 1

Circuit diagram: 2 Marks
Each subpart: 1 Mark each

The required circuit diagram is shown below.

Resistance of the parallel combination,
$R=\frac{1}{\frac{1}{3}+\frac{1}{6}}=\frac{6}{2+1}=\frac{6}{3}=2\Omega$
(a) If R' is the equivalent resistance of the circuit.
$\therefore$ R'= 10 + R = 10 + 2 = $12\Omega$
Now, $I=\frac{3}{12}=\frac{1}{4}=0.25A$
$[ByOh{m}^{\prime }slawI=\frac{V}{R^{\prime }},]$
(b) Since potential difference across $3\Omega$ resistor is equal to potential difference across R (parallel combination of $3\Omega$ and $6\Omega$).
$\therefore V_1=IR=0.25\times 2=0.5V$
(c) Current flowing through $3\Omega$ resistor,$I_1=\frac{V_1}{3}=\frac{0.5}{3}=0.17A$