SOLUTIONS
Homework 2 (Unit 1)
(Total of 100 points)
1. (20 points)
Solve this linear equation for w:
0.28 = 0.04(w-1.0)
SOLUTION:
0.28 – 0.04W - 0.04
0.28+0.04 = 0.04 W
0.32=0.04W
Dividing both sides by 0.04 yields: W=8
2. (20 points)
Solve this linear equation for R:
SOLUTION:
Multiplying by 2 on both sides of the equation, yields:
R-4R=12
-3R=12
R=-4
We can substitute -4 in for R to check our work:
So -2-8=6 (It is not necessary to show this check to obtain full credit.)
3. (20 points)
The voltage-current relationship for the circuit shown in the figure is given
by Ohm’s Law, V=IR, where V is the applied voltage in volts, I is the current
in amps, and R is the resistance of the resistor in ohms.
a. Sketch the graph of I as a function of V if the resistance is 5
SOLUTION (15 points):
Rearranging the equation we get I(V) as follows:
V(I) = IR  I(V) = V
I(V) is a linear equation of basic form, y(x) = mx + b, where the y-intercept is
b=0.
Thus we see that the slope is m = = =
So we can plot i(V) = V as follows.
b. Find the current I if the applied voltage is 10 V.
SOLUTION (5 points):
For V=10V, I(10)= (10) = 2A=I(10), which matches the plot.
4. (20 points)
A voltage source Vs is used to apply two different voltages (12V and 18V) to
the single-loop circuit shown in the figure. The values of the measured
current are shown in the table. The voltage and current satisfy the linear
relationship Vs = IR + V, where R is the resistance is ohms, I is the current
in amps, and Vs is the voltage in volts.
a. Using the data in the table, find the equation of the line for Vs as a
function of I, and determine the values of R and V.
SOLUTION (10 points):
Vs (I) = IR +V  Vs (I) = RI + V  y(x) = mx +b
Thus we can compute the resistance, R1 , as the slope,
R=
=
=
=8
=R
Now, Vs (I) = 12 I + V can be computed as the y-intercept by substituting
one of the data points
18 = 8(1.5) + V  6 volts
The total equation of the line is: Vs (I) = 8I +6 volts
b. Sketch the graph of Vs as a function of I and clearly indicate the
resistance R and the voltage V on the graph.
SOLUTION (10 points):
5. (20 points)
For the electric circuit shown in the figure below, the relationship between
the voltage, V, and the applied current I, is giving by
V = (I+Io) R. Find the values of R and Io if the voltage across the resistor, V, is
known for the two different values of the current shown in the table.
SOLUTION:
The voltage-current relationship V = RI + R I0 is the equation of a straight
line y=mx+b, where the slope m=R can be found from the data given in the
table as:
R=
=
=
= 10
Therefore V = 10(I) +10 I0.
The y-intercept b=10 I0 can be found by substituting the second data point
(2.2, 0.2) into V = 10(I) +10 I0
As
2.2 = 10 * 0.2 + 10 I0.
Solving for I0 gives 10 I0 = 2.2 -2 = 0.2
Which gives I0 =0.02 A
Therefore, V = 10 I +0.2; and R=10
and I0 = 0.02 A.