How to Find the Reading of Voltmeters in a Circuit with Identical Resistors?

[utkarshakash]

Homework Statement

In the circuit shown below, all three voltmeters are ideal and identical. Each resistor has the same given resistance R. Voltage V is also given. Find the reading of each voltmeter.

The Attempt at a Solution

i = 2V/3R
Applying Kirchhoff's Law to BACDE
V1+V2=0

Loop CDHFG
V1+V3=2V/3

Loop DEH
V2+V3=2V/3

Solving these three, I get incorrect answers.

 

[phyzguy]

You've calculated I incorrectly. Since the voltage V appears across 3 R's in series, I = V/(3R).

 

[utkarshakash]

You've calculated I incorrectly. Since the voltage V appears across 3 R's in series, I = V/(3R).

Oops! I used incorrect notation for current. The current in the circuit as a whole is 2V/3R. The currrents in individual branches are V/3R.

 

[phyzguy]

Oops! I used incorrect notation for current. The current in the circuit as a whole is 2V/3R. The currrents in individual branches are V/3R.

Correct. Does this solve your original problem?

 

[utkarshakash]

Correct. Does this solve your original problem?

No. The correct answers are V1=V2=V/9 and V3=2V/9

 

[phyzguy]

No. The correct answers are V1=V2=V/9 and V3=2V/9

If you've posted the problem correctly, I don't think that can be the correct answer. VC = VE = V/3, so V1 and V2 should both read 0 and V3 should read V/3.