E245 Homework 1
:
DC Circuits
Solutions
Instructions
•
Print your name clearly.
If not readable, it may be impossible to assign a grade to your
work.
•
Show solutions neatly and show all steps in solving the problem.
If solutions are not
readable, a grade can not be assigned.
If all steps in solving a problem are not shown,
partial credit can not be assigned.
•
You may find the notes at the end of the set of problems helpful.
A.
Problems to be solved
Problem 1:
For the circuit in Figure 1 below, determine the equivalent resistance (illustrated in Figure 1b)
between output points A and B by combining resistors in parallel and combining resistors in
series in the starting circuit of Figure 1a.
Show all steps in your reduction to a single equivalent
resistance (e.g., what resistors are combined and the value when combined for each step along
the way to the final answer).
You may find it useful to redraw the circuit as you proceed through
the combining of resistors.
SOLUTION:
•
R5 and R7 are in parallel.
RA = (R5 * R7)/(R5 + R7) = (3 * 6)/(3 + 6) = 2 ohms
•
R4 and RA are in series
RB = R4 + RA = 1 + 2 = 3 ohms
•
R6 and RB are in parallel
RC = (R6 * RB)/(R6 + RB) = (6 * 3)/(6 + 3) = 2 ohms
•
R2, RC, and R3 are in series
RD = R2 + RC + R3 = 3 + 2 + 1 = 6 ohms
•
R1 and RD are in parallel
Req = (R1 * RD)/(R1 + RD) = (3 * 6)/(3 + 6) = 2 ohms
RETURN THIS FRONT PAGE AS PAGE ONE OF YOUR SOLUTIONS
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View Full DocumentR2
R1
R3
R5
R6
A
B
R7
R4
R1 = 3 ohms
R2 = 3 ohms
R3 = 1 ohm
R4 = 1 ohm
R5 = 3 ohms
R6 = 6 ohms
R7 = 6 ohms
A
B
R
eq
Equivalent Resistance
(a)
(b)
Figure 1
Problem 2:
Figure 2a is similar to Figure 1a but replaces R6 with a current source I
A
= 2 amps and adds a
voltage source V
A
= 3 Volts in the loop containing R7.
Again, you are to determine the
equivalent resistance between points A and B.
To do this, you need to replace the current and
voltage sources by their equivalent resistances.
Answer the following questions.
•
What is the resistance of a current source?
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 Spring '08
 Tang
 Ohms, Resistor, SEPTA Regional Rail, Electrical resistance

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