Question

Two resistors of \(4 \Omega\) and \(6 \Omega\) are connected in parallel to a cell to draw a current of 0.5 A from the cell.

1. Draw a labelled diagram showing the above arrangement.
2. Calculate the current in each resistor.

Answer 1

(i) Connect both resistors across the same two terminals of the cell; the ammeter measures the total current in series with the source:

(ii) Given: \(R_1=4\,\Omega\)

\(R_2=6\,\Omega\)

\(I=0.5\,A\)

The equivalent resistance is:

\[ R=\frac{R_1R_2}{R_1+R_2}\]

\[=\frac{4\times6}{4+6}\]

\[=2.4\ \Omega\]

The potential difference across the parallel pair is:

\[V=IR\]

\[=0.5\times2.4\]

\[=1.2\ \mathrm{V}\]

Current through the 4 Ω resistor:

\[ I_1=\frac{V}{R_1} \]

\[=\frac{1.2}{4}\]

\[=0.3\ \mathrm{A}\]

Current through the 6 Ω resistor:

\[ I_2=\frac{V}{R_2}\]

\[=\frac{1.2}{6}\]

\[=0.2\ \mathrm{A}\]