In a parallel circuit, with a number of resistors, the voltage across each resistor is ________

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Examoogle · Accepted Answer

The same for all resistors

Explanation: In a parallel circuit, all components are connected across the same two nodes, ensuring that the potential difference across each branch is identical. Consequently, the voltage across each resistor is equal to the source voltage applied to the circuit.

Working Principle: Because every resistor in a parallel network shares the same two terminal connection points (nodes), there is no series impedance between the voltage source and the individual components. By Kirchhoff's Voltage Law (KVL), the sum of voltages around any closed loop is zero, and since each resistor forms a closed loop with the source, the voltage drop across each must equal the source voltage.

Key Formulas: $V_{total} = V_1 = V_2 = V_n$ — The voltage across all parallel branches is equal.; $I_{total} = \sum_{i=1}^{n} I_i = \sum_{i=1}^{n} \frac{V}{R_i}$ — Kirchhoff's Current Law showing individual branch currents depend on resistance.

Key Points: Parallel connection maintains constant voltage across all branches.; The total resistance of a parallel circuit is always less than the smallest individual resistor.; Current in each branch is inversely proportional to its resistance ($I \propto \frac{1}{R}$).

Advantages: Independent operation of branches; if one component fails, others remain energized.; Total power handling capacity of the circuit increases.

Disadvantages: Requires more wiring/cabling compared to series circuits.; Total current increases significantly with additional parallel branches, potentially overloading the source.

Applications: Residential wiring (every appliance is rated for the same line voltage, e.g., 230V).; Power distribution systems.

Additional Info: In a series circuit, voltage is divided according to the resistance ratio ($V_i = V_{total} \cdot \frac{R_i}{R_{total}}$).. Option B and C describe characteristics of components in a series circuit.

Answer: A is correct — The voltage across all resistors connected in parallel is identical to the applied source voltage.

Exam Tip: Remember: Parallel = Constant Voltage; Series = Constant Current.

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