A circuit contains two un-equal resistances in parallel

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Examoogle · Accepted Answer

potential difference across each is same

Explanation: In a parallel circuit configuration, the terminals of all components are connected to the same two nodes. Consequently, the potential difference (voltage) across every branch connected in parallel must be identical, regardless of the individual resistance values.

Working Principle: According to Kirchhoff's Voltage Law (KVL) applied to parallel branches, the voltage source connected across the parallel combination appears directly across each resistor. While the voltage remains constant ($V_1 = V_2 = V$), the current through each branch is inversely proportional to its resistance, governed by Ohm's Law, $I = V/R$.

Key Formulas: $V = I_1 R_1 = I_2 R_2$ — Equality of potential in parallel branches; $I_{total} = I_1 + I_2 = \frac{V}{R_1} + \frac{V}{R_2}$ — Total current in parallel circuit

Key Points: Voltage is the common parameter in parallel circuits.; Current divides in parallel circuits based on $I \propto \frac{1}{R}$.; Total equivalent resistance $R_{eq}$ is always less than the smallest individual resistance.; Conductance $G = \frac{1}{R}$ is additive in parallel: $G_{eq} = G_1 + G_2$.

Advantages: Independent operation of branches.; Constant voltage supply to all loads.

Disadvantages: Requires more wiring than series circuits.; High current demand if total resistance becomes very low.

Applications: Domestic wiring systems.; Distribution networks in power systems.

Additional Info: Option A is incorrect because current depends on resistance ($I = V/R$); only with equal resistance would currents be equal.. Option B is incorrect because current is inversely proportional to resistance; therefore, larger current flows in the smaller resistor.. Option D is incorrect because smaller resistance has larger conductance, as conductance is the reciprocal of resistance ($G = 1/R$).

Answer: C is correct — In a parallel circuit, the potential difference across each branch is identical as they share the same two junction nodes.

Exam Tip: Always remember: Series circuits divide voltage, while parallel circuits divide current.

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