Question

Study the adjoining diagram carefully and answer the following questions:

1. By using the reading of voltmeter and ammeter, calculate the equivalent resistance of 40 Ω and R.
2. Calculate the value of R.
3. Calculate the current flowing through R.

Answer 1

(i) Equivalent resistance:

The voltmeter reads the potential difference across the parallel combination, and the ammeter reads the total current.

\[ \mathrm{R}_{eq} = \frac{\mathrm{V}}{\mathrm{I}} \]

\[ = \frac{4.0 \ \text{V}}{0.4 \ \text{A}} \]

\[ = 10 \ \Omega \]

(ii) Value of R:

For resistors in parallel:

\[ \frac{1}{\mathrm{R}_{eq}} = \frac{1}{40 \ \Omega} + \frac{1}{\mathrm{R}} \]

\[ \frac{1}{10} = \frac{1}{40} + \frac{1}{\mathrm{R}} \]

\[ \frac{1}{\mathrm{R}} = \frac{1}{10} - \frac{1}{40} \]

\[ = \frac{4 - 1}{40} \]

\[ = \frac{3}{40} \]

\[ \therefore \mathrm{R} = \frac{40}{3} \ \Omega \]

\[ \approx 13.3 \ \Omega \]

(iii) Current through R:

Both resistors in parallel have the same potential difference, which is 4.0 V.

\[ \mathrm{I}_{R} = \frac{\mathrm{V}}{\mathrm{R}} \]

\[ = \frac{4.0}{\frac{40}{3}} \]

\[ = \frac{4.0 \times 3}{40} \]

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

Therefore, the current flowing through R is 0.3 A.