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

Answer 1

The voltage across each resistor is constant or unchanged.
This is because, if the resistances are in parallel connection , then they must be across same potential difference, which is remaining constant in this case.
And , if the resistances are in series, then let resistance of each of n resistors in series be R, the voltage source be V, and the current through each resistance be I.
So, equivalent resistance is nR.
Thus, from Ohm's law , I = V/nR. So, voltage across each resistor is (V/nR)×R = V/n.
Now, when each resistor is doubled i.e. 2R, then the equivalent resistance is 2nR.
So, I = V/2nR. Thus, voltage across each resistor is (V/2nR)×2R =V/n.
Thus, the voltage across each resistor is remaining unchanged.

Answer 2

Given:

• The value of all the resistors is doubled.

To Find:

• The voltage across each resistor.

Solution:

Using Ohm's law, V = R×I where 'V' is the voltage, 'R' is the resistance, and 'I' is the current.

It is already given that, R = 2R

∴ V = 2R×I ⇒ V/2R = I

Here, the current through each resistor will be half when the resistance is doubled therefore the voltage across each resistor will remain the same since it is alreday mentioned that the linear resistors consist of ideal voltage sources.

∴ The voltage across each resistor remains unchanged.