1. Find the value of the resistor R2 (Ω) in the circuit shown below.
a) 5
b) 6
c) 7
d) 8
Explanation: As V1=100V, V2=15×2=30V, V3=40V. (V1-V2)/14+(V1-V3)/R2=15. On solving we get R2 = 6Ω.
2. Find the voltage (V) at node 1 in the circuit shown.
a) 5.32
b) 6.32
c) 7.32
d) 8.32
Explanation: At node 1, (1/1+1/2+1/3)V1-(1/3)V2 = 10/1. At node 2, -(1/3)V1+(1/3+1/6+1/5)V2 = 2/5+5/6. On solving above equations, we get V1=6.32V.
3. Find the voltage (V) at node 2 in the circuit shown below.
a) 2.7
b) 3.7
c) 4.7
d) 5.7
Explanation: At node 1, (1/1+1/2+1/3)V1-(1/3)V2 = 10/1. At node 2, -(1/3)V1+(1/3+1/6+1/5)V2 = 2/5+5/6. On solving above equations, we get V2=4.7V.
4. Find the voltage at node 1 of the circuit shown below.
a) 32.7
b) 33.7
c) 34.7
d) 35.7
Explanation: Applying Kirchhoff’s current law at node 1, 10 = V1/10+(V1-V2)/3. At node 2, (V2-V1)/3+V2/5+(V2-10)/1=0. On solving the above equations, we get V1=33.7V.
5. Find the voltage at node 2 of the circuit shown below.
a) 13
b) 14
c) 15
d) 16
Explanation: Applying Kirchhoff’s current law at node 1, 10 = V1/10+(V1-V2)/3. At node 2, (V2-V1)/3+V2/5+(V2-10)/1=0. On solving the above equations, we get V2=14V.
6. Consider the figure shown below. Find the voltage (V) at node 1.
a) 13
b) 14
c) 15
d) 16
Explanation: Applying Super Node Analysis, the combined equation of node 1 and node 2 is (V1-V3)/3+3+(V2-V3)/1-6+V2/5=0. At node 3, (V3-V1)/3+(V3-V2)/1+V3/2=0. Also V1-V2=10. On solving above equations, we get V1 = 13.72V ≈ 14V.
7. Consider the figure shown below. Find the voltage (V) at node 2.
a) 3
b) 4
c) 5
d) 6
Explanation: Applying Super Node Analysis, the combined equation of node 1 and node 2 is (V1-V3)/3+3+(V2-V3)/1-6+V2/5=0. At node 3, (V3-V1)/3+(V3-V2)/1+V3/2=0. Also V1-V2=10. On solving above equations, we get V2 = 3.72V ≈ 4V.
8. Consider the figure shown below. Find the voltage (V) at node 3.
a) 4.5
b) 5.5
c) 6.5
d) 7.5
Explanation: Applying Super Node Analysis, the combined equation of node 1 and node 2 is (V1-V3)/3+3+(V2-V3)/1-6+V2/5=0. At node 3, (V3-V1)/3+(V3-V2)/1+V3/2=0. Also V1-V2=10. On solving above equations, we get V3 = 4.5V.
9. Consider the figure shown below. Find the power (W) delivered by the source 6A.
a) 20.3
b) 21.3
c) 22.3
d) 24.3
Explanation: The term power is defined as the product of voltage and current and the power delivered by the source (6A) = V2x6 = 3.72×6 = 22.32W.
10. Find the voltage (V) at node 1 in the circuit shown below.
a) 18
b) 19
c) 20
d) 21
Explanation: The equation at node 1 is 10 = V1/3+(V1-V2)/2. According to super Node analysis, (V1-V2)/2=V2/1+(V3-10)/5+V3/2V2-V3=20. On solving, we get, V1=19V.