A circuit has three branches with resistors: 2 ohms, 4 ohms, and 8 ohms in parallel. Which statement correctly describes the current through the 2 ohm resistor compared to the 8 ohm resistor?
The current through the 2 ohm resistor is greater than that through the 8 ohm resistor
In a parallel circuit, every branch has the same voltage V across it.
By Ohm’s law, the branch current is \(I = \frac{V}{R}\), so current is inversely proportional to resistance.
\(I_2 = \frac{V}{2}\) and \(I_8 = \frac{V}{8}\), so \(\frac{I_2}{I_8} = 4\) — the 2 Ω branch carries four times the current of the 8 Ω branch.
The other statements fail: no branch current is zero because each resistor has the full voltage across it; currents are equal only when resistances are equal; and a smaller resistance carries more current, not less.
Hence, the answer is The current through the 2 ohm resistor is greater than that through the 8 ohm resistor.
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Important Questions from Series and Parallel Connection of Resistance
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If n identical resistance, each of resistance R, are connected in parallel, the equivalent resistance is:
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For the figure shown below, find the value of conductance 'G' (in S).
