## 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.

**Solution**

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 *V*_{1}.

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

(*V*_{1}-2e)/2*r* + (*V*_{1}-e)/*r* + *V*_{1}/*R* = 0

(*V*_{1}-3.0)/0.4 + (*V*_{1}-1.5)/0.2 + *V*_{1}/7.0 = 0

1.4(*V*_{1}-3.0) + 2.8(*V*_{1}-1.5) + 0.08*V*_{1} = 0

4.28*V*_{1} = 8.4

*V*_{1} = 1.96 V

Thus the current through *R* is *V*_{1}/*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.