Question

The diagram above shows three resistors connected across a cell of e.m.f. 1.8 V and internal resistance \(r\). Calculate:

1. current through \(3 \Omega\) resistor.
2. the internal resistance \(r\).

Answer 1

Given: EMF, \(E=1.8\,V\)

Total current, \(I=0.3\,A\)

Resistors: \(3\,\Omega,\ 1.5\,\Omega,\ 4\,\Omega\)

(i) Current through 3 Ω resistor,

The 3 Ω and 1.5 Ω resistors are connected in parallel.

\[ R_p=\frac{3\times1.5}{3+1.5}\]

= 1 Ω

Voltage across the parallel combination,

\[ V=IR_p=0.3\times1\]

\[=0.3\times1\]

= 0.3 V

Current through 3 Ω resistor:

\[ I_1=\frac{V}{R}\]

\[=\frac{0.3}{3} \]

\[{=0.1\,A} \]

(ii) Internal resistance (r):

External resistance,

\[ R=1+4\]

\[=5\,\Omega \]

Using the formula,

\[ E=I(R+r) \]

\[1.8 = 0.3(5+r) \]

\[\frac{1.8}{0.3}=5+r\]

\[r = 6 - 5\]

\[{\therefore r=1\,\Omega}\]