The terminal voltages of a cell are found to be 29 V and 28 V when it delivers currents of 1 A and 2 A, respectively. The emf and the internal resistance of the cell are, respectively
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30 V; 1 Ω
Given:
Terminal voltages: $V_1 = 29\ \text{V}$ at $I_1 = 1\ \text{A}$, $V_2 = 28\ \text{V}$ at $I_2 = 2\ \text{A}$
Terminal voltage: $V = \mathcal{E} - I r$, where $\mathcal{E}$ = emf, $r$ = internal resistance.
Set up equations:
$29 = \mathcal{E} - 1 \cdot r$
$28 = \mathcal{E} - 2 \cdot r$
Subtract second equation from first:
$29 - 28 = (\mathcal{E} - r) - (\mathcal{E} - 2r)$
$1 = r$
∴ Internal resistance, $r = 1\ \Omega$
Substitute $r$ in first equation:
$29 = \mathcal{E} - 1 \Rightarrow \mathcal{E} = 30\ \text{V}$
∴ Emf = 30 V, Internal resistance = 1 Ω