Question

A network contains linear resistors and ideal voltage sources. If values of all the resistors are doubled, then the voltage across each resistor is

• A. halved
• B. doubled
• C. increased by four times
• D. not changed

Hint:

In linear circuits with ideal voltage sources, scaling all resistances equally does not change voltage distribution—only currents change.

Answer 1

The Correct Option is D

Step 1: Understanding the given network.
The network consists of linear resistors and ideal voltage sources. Ideal voltage sources maintain a fixed voltage regardless of the current drawn from them.
Step 2: Effect of doubling resistances.
When all resistances in the circuit are doubled, the total resistance of the circuit increases. As a result, the current flowing in the circuit decreases according to Ohm’s law.
Step 3: Voltage across each resistor.
Although the current decreases, the voltage distribution in a linear resistive network with ideal voltage sources depends only on the ratio of resistances, not their absolute values. Since all resistances are scaled by the same factor, their ratios remain unchanged.
Step 4: Analyzing the options.
(A) Voltage is not halved because voltage division ratios remain the same.
(B) Voltage does not double since source voltages are unchanged.
(C) Voltage cannot increase four times without change in source voltage.
(D) Correct — the voltage across each resistor remains unchanged.
Step 5: Final conclusion.
Thus, even after doubling all resistances, the voltage across each resistor remains the same.