Kirchhoff's Voltage Law in Parallel Circuits

Steps:

• Identify the circuit: Resistors R1, R2, R3 in parallel across cell with emf V, so each branch shares the same potential difference.
• Apply Kirchhoff's second law (KVL): Sum of voltages in any closed loop equals zero.
• Consider a loop through the cell and one resistor, e.g., cell to R1: +V - V1 = 0, so V = V1.
• Repeat for other branches: V = V2 and V = V3, yielding V = V1 = V2 = V3.

Why D is correct:

• In parallel circuits, KVL requires the cell's emf V equals the voltage drop across each resistor, as each forms a loop where V - Vi = 0.

Why the others are wrong:

• A: This is Kirchhoff's first law (current law) for currents at the junction.
• B: This applies to series circuits, where voltages add up.
• C: This implies V2 exceeds the others, violating equal voltages in parallel.

Final answer: D