Circuits
Fall 2014
ECSE-2010
Name _____________________
Homework 1
Due: September 4, 2014
1) Which of the following charge densities correspond to a continuous current as a
function of time. (A continuous current has no jump discontinuities or sudden changes in
value).
0 [C]
t0

a) qt   
0.0000005 exp  1E 3t  [C] 0  t
0 [C] t  0
b) qt   
(this one is a little tricky)
1 [C] 0  t
c) qt   1E  12 t exp  1E6t   1E  18 exp  1E6t [C]
Plot/sketch the current for all three cases to justify your answer.
2) Source devices
4
R1
2k
V1
I1
1E-3
a) Determine the current through the voltage source, V1. Include the direction in
your answer. (Answer check: IV1 = 1mA, upward)
b) Determine the voltage across the current source, I1. Include the polarity in your
answer.
Vunknown
I2
2E-3
R2
5k
c) Determine a value for Vunknown such that the current through voltage source is
zero.
d) Considering your answer to part c, how much power is supplied by the current
source? (Answer check: PI2 = -20mW, power produced)
e) How much power is supplied by the voltage source?
f) How much power is dissipated by the resistor?
S. Sawyer
Rensselaer Polytechnic Institute
Revised: 8/24/2014
Troy, New York, USA
1
Circuits
Fall 2014
ECSE-2010
Name _____________________
3) Nodal voltages/voltage drops/currents
B
R2
R3
1k
3k
I2
2mA
A
I1
1mA
4
V2
R1
V3
2k
1
2
C
V1
R4
1k
0
a)
b)
c)
d)
e)
How many nodes are in the above circuit? (Answer check: six)
For the indicated ground, determine the voltage at nodes A, B, and C
Determine the voltage across I2 and R3 (Answer check: VR3 = 5V)
Determine the current through R4 and V3
Determine the power produced or consumed by V3 and I2.
S. Sawyer
Rensselaer Polytechnic Institute
Revised: 8/24/2014
Troy, New York, USA
2
Circuits
Fall 2014
ECSE-2010
Name _____________________
4) KCL/KVL
R1
2k
I1
5
V1
3E-3
R2
4k
R3
2k
In the above circuit,
a) Assign (guess) a polarity for each resistor. Include a current ‘arrow’ that is
consistent with that polarity.
b) Determine three linearly independent equations for the voltage across the
resistors. You will have to use a combination of Ohm’s Law, KCL and KVL.
Make sure you are careful to use the assumed polarity from part a when setting up
your equations.
c) Set up these equations in matrix/vector form.
d) Solve for the voltages across each resistor, including the sign based on your
polarity ‘guess’. (Answer check: VR1 = 0.6V, current flowing to the ‘right’)
e) Fill in the following table. Remember, positive power corresponds to power
consumed/dissipated and negative power corresponds to power produced.
f) Verify that power produced equals power consumed/dissipated.
Voltage [V]
Current [mA]
Power [mW]
R1
R2
R3
V1
I1
S. Sawyer
Rensselaer Polytechnic Institute
Revised: 8/24/2014
Troy, New York, USA
3
Circuits
Fall 2014
ECSE-2010
Name _____________________
5) KCL/KVL
R3
4k
4
V1
R5
R1
1k
10k
10E-3
I1
R4
4k
R2
2k
In the above circuit,
a) Determine five linearly independent equations for the voltage across the resistors.
You will have to use a combination of Ohm’s Law, KCL and KVL.
VR 4 VR 2

0)
(Answer check: one of the equations applying KCL, 0.01 
4000 2000
b) Set up these equations in matrix/vector form.
c) Solve for the voltages across each resistor. I suggest using Maple or Matlab (or
any other equivalent tool, there are lots of matrix solvers online).
S. Sawyer
Rensselaer Polytechnic Institute
Revised: 8/24/2014
Troy, New York, USA
4