EE331– Exam 1 – 2005 (see the note at the end)
1. Write the name of each symbol beside the number for that symbol – see the help box.
_ind current source
1
_ind voltage source 2
_dep current source 3
+
+
_dep voltage source 4
–
_resistor
5
–
_switch
6
_battery
7
1
2
3
4
5
6
7
8
9
10
_inductor
8
Help - diode, transistor, battery, resistor, switch, relay, FET,
_capacitor
9
independent (ind.) current source, ind. voltage source,
_diode
10
crossing wires, connecting wires, dependent voltage source,
_ground
11
11
12
13
dependent current source, inductor, ground, transformer,
wall plug, terminal, capacitor.
_crossing wires
12
_connected wires
13
2. Is the element absorbing power, supplying power, or neither (0 watts)?
v1
v2
v1 ≠ v2
i<0
Ans:__absorb______
______
vR +
–
Ans:__absorb______
______
vR = 0
+
10 A
Ans:___supply_____
______
10 V
+ –
i>0
10 A
Ans:___neither_____
______
Ans:___neither_____
______
–
Ans:___absorb_____
______
3. Three resistors of 2 ohms each are in series with one end grounded and the other end has a 12 volt
battery with the + terminal tied to the resistors and the negative end of the battery is grounded.
Draw a diagram in the space below for this circuit.
2
2
+ 2
i
12 V
What is the total resistance RT of the circuit that the battery “sees”? Show an equation and the
answer.
Rt = 2+2+2 = 6 ohms
Show the battery current
i
on the diagram and calculate its value. Show the math and your answer.
i = 12/6 = 2 amps
Use ohm’s law to calculate the voltage drop in the resistor tied to ground. Show the math and the
answer.
v = iR = (2)(2) = 4 volts
1
EE331– Exam 1 – 2005 (see the note at the end)
Use the voltage divider equation to calculate the voltage in the resistor tied to ground. Show the
math and your answer (hint: same answer).
v = (12)(2/6) = (12)/(3) = 4 volts
How much power is the battery supplying? Show the math and the answer.
P = vi = (12)(2) = 24 watts
If the battery has 1 amp-hour of energy left in it, how long will the battery supply this current until
it “runs down”? Show the math and your answer.
1 A-H/2 A = .5 hours
What will be the battery voltage after the battery is “run down”?
0 volts
4. Convert the Thevenin voltage source below to an equivalent Norton current source. Draw a new
diagram and show all the values of the equivalent source (and the resistance) and include the
direction of the current in the current source and its magnitude. Show how you calculated this
current using ohm’s law:
5
I = 10/5 = 2 A
10 V
+
–
5
I
5. Write the KCL nodal equations for the circuit below either in matrix form or conventional KCL
equations for each node. Make the node voltages the variables in the equations. Write an equation
for calculating the current i12 in terms of the nodal voltages v1 and v2. Find node voltages and the
current i12 .
1
v1
v2
1
½+1
-1
v1
=
1
i12
1
2
1
2
-1
½+1
i12 = (v1 – v2)/1
v2
v1 = 2 volts v2 = 2 volts
i12 = 0 amps
2
EE331– Exam 1 – 2005 (see the note at the end)
6. Write the KVL loop equations for the circuit below. Either in matrix form or conventional KVL
equations for each loop is acceptable. Make the loop currents variables in the equations. Do not
solve the equations. Write an equation for calculating the voltage v1 in terms of the loop currents.
1
3
v1
5
4
10
+
–
i1
i2
i3
2
10
=
3
–2
0
i1
0
=
–2
9
–4
i2
-5
=
0
–4
9
i3
+
–
5
v1 = 2(i1 – i2) or v1 = 10 – 1(i1)
Useful formulas:
Conductance: G(mhos) = 1/R(ohms)
Ohm’s law: V=IR I=V/R R=V/I
Power:
P = IV = I2R = V2/R
Kirchhoff’s current law:  i's = 0 (at a node)
Kirchhoff’s voltage law:  v's = 0 (around a loop)
Parallel R formula: Req=1/(1/R1+1/R2+1/R3+…)
Series R formula: Req=R1+R2+R3+…
Voltage divider formula: v1 = Vin( R1/R) (the R’s are all in series)
matrix form of nodal equations for KCL
matrix form of loop equations for KVL
where G12=1/R12 of the R from node 1 to 2
where R12 is common to loops 1 and 2
Note that any homework problem or material in the lectures could be on the next Test 1.
3