Assignment 2
Electric Circuit Analysis
EE-116
Instructions: The answers submitted MUST be in the same order as the
questions.
Part A- Energy storage Elements
Q1. A capacitor is charged by a constant current of 2mA and results in a voltage increase
of 5V in a 10s interval. What is the value of the capacitance?
Q2. The voltage v(t) across a 2μF capacitor is given by the waveform as shown in Fig. 1. Find
a) The equations for v(t)
b) The equations for i(t)
c) Sketch the current waveform.
Figure 1
Q3. The current i(t) in a 10mH inductor is shown below in Fig. 2. Find
a) The equations for i(t)
b) The equations for v(t)
c) Sketch the voltage waveform
Figure 2
Q4. Find equivalent inductance across nodes A and B
Figure 3
Q5. Find equivalent inductance across nodes a and b
Figure 4
Q6. Find equivalent Capacitance across nodes A and B
Figure 5
Part B- Transient and Steady State response
Q7. Assume the circuit given in Fig. 6. The capacitor has been connected to the circuit as can be
seen for a long time. At time t = 0 the switch is disconnected ibn the direction as shown by the
arrow. For this circuit find
a) 𝑉𝑐 𝑎𝑡 𝑡 = 0−
b) 𝑉𝑐 𝑎𝑡 𝑡 = 0+
c) 𝑉𝑐 (𝑡)
Figure 6
Q8. Assume the circuit given in Fig. 7. The capacitor has been connected to the circuit as can be
seen for a long time. At time t = 0 the switch is disconnected ibn the direction as shown by the
arrow. For this circuit find
a) 𝑉𝑐 𝑎𝑡 𝑡 = 0−
b) 𝑉𝑐 𝑎𝑡 𝑡 = 0+
c) 𝑉𝑐 (𝑡)
Figure 7
Part C- AC Circuits
Q9. Calculate i(t), the time-domain current in the capacitor shown in the following circuit
if the voltage is:
a) v1(t) = 8 cos (377t – 30) V
b) v2(t) = 4 cos (377t + 60) V
Q10. Calculate i(t), the time-domain current in the inductor in the following circuit for the
following voltage inputs:
a) v1(t) = 24 cos (377t + 12) V
b) v2(t) = 18 cos (377t + 48) V
Q11. Find the frequency-domain impedance, Z, of the following networks:
a)
Q12. For the circuit shown below, vs(t) = 120 cos (377t) V. Find
a) vR(t)
b) vL(t)
Problem Based Learning (PBL)
Part D – 2nd Order differential equation
Q13. For the circuit shown below R = 2kΩ, C = 1µF and L = 10mH.
a) For this circuit find 𝜔𝑜 , ζ assuming 𝑣𝑠 = 0 (Natural response)
b) Find the second order differential equation for i(t), the series current in this circuit for natural
response of the circuit.
c) Analyze the values of ζ and comment on the behavior of i(t) based on the value of ζ for natural
response of the circuit.
d) Assuming 𝑣𝑠 = 5 cos (1000𝑡 + 20), draw this circuit on Proteas or Spice and plot i(t). Attach
the plots
e) Comment of the shape of the plot with respect to the value of ζ and compare it with your
comments from part c.