Question

Four cells each of EMF 2V and internal resistance $0.1\Omega$ are connected in series. The combination is connected in series to an ammeter of negligible resistance, a $1.6\Omega$ resistor and an unknown resistor $R_1$. The current in the circuit is 2A. Draw a labelled circuit diagram for the arrangement and calculate the:
(a) value of $R_1$.
(b) potential difference across $R_1$
[5 MARKS]

Answer 1

Circuit diagram: 2 Marks
Each subpart: 1.5 Marks each

The labelled circuit diagram is shown below.

(a) Total resistance = 1.6 + 0.1 $\times$ 4 + $R_1$
= 1.6 + 0.4 + $R_1$ = 2 + $R_1$
Total EMF = 2+2+2+2=8V
We know that I $=\frac{TotalEMF}{Totalresistance}$
$\therefore 2=\frac{8}{R_1+2}$
or $2R_1+4=8$
or $2R_1=8-4=4$
or $R_1=2\Omega$
$\therefore$ Total resistance = $R_1+2$
$=2+2=4\Omega$
(b) Potential difference across $R_1=I{R}_1$
$=2\times 2=4V$