A circuit contains two un-equal resistances in parallel

Question

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Option C: potential difference across each is same

Explanation & Concepts:
In any parallel electrical circuit, the potential difference across all individual branches must be identical because they are connected between the same two nodes. This property is fundamental to the definition of a parallel connection, regardless of the individual resistance values.

Working Principle: According to Kirchhoff's Voltage Law and the definition of a parallel circuit, every branch connected in parallel across a supply voltage $V$ experiences the exact same potential difference $V_{branch} = V_{total}$. While the potential is constant, current divides according to Ohm's Law ($I = \frac{V}{R}$), meaning current is inversely proportional to resistance.

Key Formulas: $V_{parallel} = V_1 = V_2 = ... = V_n$ — The voltage across parallel branches is constant.; $I = \frac{V}{R}$ — Ohm's Law, determining branch current distribution.

Key Points: Parallel connection ensures equipotential nodes.; Current is inversely proportional to resistance ($I \propto \frac{1}{R}$).; Conductance ($G = \frac{1}{R}$) is higher for smaller resistances, leading to higher current flow.; The total equivalent resistance is always lower than the smallest individual resistance.

Advantages: Individual components can be controlled independently.; Failure of one branch does not stop current in other branches.

Disadvantages: Requires more wiring compared to series circuits.; Total current increases as more branches are added, risking overload.

Applications: Domestic wiring (household appliances); Power distribution systems

Additional Info: Option A is incorrect because current splits based on Ohm's Law.. Option B is incorrect because larger resistance draws smaller current ($I = \frac{V}{R}$).. Option D is incorrect because conductance $G = \frac{1}{R}$; thus, smaller $R$ means larger $G$.

Answer: C is correct — In a parallel circuit, the voltage across each branch is identical regardless of the resistances.

Exam Tip: Remember: Parallel = Voltage is same; Series = Current is same. This simple mnemonic is the key to solving most DC circuit analysis problems in competitive exams.

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Option A: current is same in both

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Option B: large current flows in larger resistance

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Option D: smaller resistance has smaller conductance

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