## PHYS345 Electricity and Electronics

Quiz 2: dc Circuit Analysis

This circuit was suggested as Special Problem 2.2 before our work with mesh and nodal analysis. Please determine the numerical value of the current through the load R by using nodal analysis.

The emf of each battery is 1.5 V, the internal resistance r of each battery is 0.2 ohm, and the load resistance R is 7.0 ohm.

Hint: the branch on the right may be simplified to consist of one emf and one resistance.

The schematic below was redrawn to consolidate the two batteries in series into one voltage source. One side of resistor R has been grounded; we seek V1.

Application of nodal analysis yields the following equation for the unknown voltage, with the circuit element parameters entered in the second equation:

(V1-2e)/2r + (V1-e)/r + V1/R = 0
(V1-3.0)/0.4 + (V1-1.5)/0.2 + V1/7.0 = 0
1.4(V1-3.0) + 2.8(V1-1.5) + 0.08V1 = 0
4.28V1 = 8.4
V1 = 1.96 V

Thus the current through R is V1/R = (1.96 V)/(7.0 V) = 0.28 A.

"http://www.physics.udel.edu/~watson/phys345/quiz/2soln.html"
Last updated Sept. 17, 1998.
Copyright George Watson, Univ. of Delaware, 1998.