Question

MIDTERM
A linear circuit is shown below.

The elements in this circuit have the following values: R1=200Ω, R2=200Ω, R3=100Ω, V1=5V, I1=0.001A and I2=0.005A
Determine the potentials at nodes A and B, assuming a ground node as shown in the figure.

(a) What is the value of voltage vA in Volts?
(b) What is the value of voltage vB in Volts?
Now let us determine if the answers you came up with satisfy the laws of physics.

What is the power (in Watts) dissipated in resistor R1?
What is the power (in Watts) dissipated in resistor R2?

Answer 1

loop law for v1, r1, r2, r3
lv1 = current from v1
Ir3 = current pass r3
- v1 + Iv1(r1) + Iv1(r2) + Ir3(r3) = 0
-5 + Iv1(200) + Iv1(200) + Ir3(100) = 0
400Iv1 = 5 - 100Ir3 ...(1)

current law at B
Iv1 + I1 - Ir3 - I2 = 0
Iv1 + 0.001 - Ir3 - 0.005 = 0
Iv1 = Ir3 + 0.004 ...(2)

solve by using (1),(2)
Ir3=0.0068A, Iv1=0.108A

Vb = Ir3(r3) = 0.0068(100) = 0.68V

Va = Vb + Iv1(r2) = 0.68 + 0.0108(200) = 0.68 + 2.16 = 2.84V

power = I^2(r)