## PHYS345 Electricity and Electronics

**Quiz 2 Solution:** dc Circuit Analysis

What is the voltage across the current source?

**Via nodal analysis:**

Defining the nodal voltages in the conventional way (with the reference node at the bottom grounded to 0 V) leads to:

- KCL at node 1:
- (V
_{1}-2)/2 + V_{1}/3 + (V_{1}-V_{2}) = 0
- KCL at node 2:
- (V
_{2}-V_{1}) + V_{2}/5 -2 = 0

- Multiplying eqn. 1 through by 6, eqn. 2 through by 5, and consolidating terms leads to the following two equations to solve:
- 11 V
_{1} - 6 V_{2} = 6
- -5 V
_{1} + 6 V_{2} = 10

- Adding the two equations produces:
- V
_{1} = 2.67 V

- Backsubstitution yields the desired answer:
- V
_{2} = 3.89 V

For this circuit, for the quantity of interest, nodal analysis is a bit quicker than mesh analysis...

"http://www.physics.udel.edu/~watson/phys345/quiz/02soln2.html"

Last updated Sept. 21, 1999.

Copyright George Watson, Univ. of Delaware, 1999.