PHYS345 Electricity and Electronics
Quiz 2 Solution: dc Circuit Analysis
What is the voltage across the current source?
Via mesh analysis:
- Defining the mesh currents in the conventional way, the KVL equation for mesh 1 is:
- 5 I1 - 3 I2 = 2.
- KVL for mesh 2:
- -3 I1 +9 I2 - 5 I3 = 0
- By inspection of mesh 3:
- I3 = -2
- Subsequent elimination of I3 in the mesh 2 equation leads to:
- -3 I1 +9 I2 = -10
- Multiplying the equation for mesh 1 by 3 yields:
- 15 I1 - 9 I2 = 6.
- Adding the two equations immediately above produces:
- I1 = -1/3 A = -0.33 A.
- Back substitution of I1 into one of the equations involving both I1 and I2 produces:
- I2 = -11/9 A = -1.22 A.
A straightforward way to find the voltage across the current source is to evaluate the voltage across the 5 ohm resistor.
The current through the resistor is I2 - I3 = 0.78 A,
thus the voltage across the resistor must be (0.78 A)(5 ohm) = 3.89 V.
Last updated Sept. 21, 1999.
Copyright George Watson, Univ. of Delaware, 1999.