Physics 142 Lecture Notes

1
ConcepTest
Circuits
Which of the equations is valid for the circuit
shown below?
1 ?
A) 2 I1 2I2 0 B) 2 2I1 2I2 4I3
0 C) 2 I1 4 2I2 0 D) I3 2I2 4I2
0 E) 2I1 I1 4I2 0
I2
2 ?
6 V
2 V
2 V
4 V
I3
I1
1 ?
3 ?
2
Algebra Test
Suppose x y 5 2 and 3x 2y 1 0. What
is x? A) zero B) 13 / 5 C) 2 / 3 D)
7 E) 17 / 4
Solve first equation for y x
y 7 y 7 x Plug
into second equation 3x 2(7 x) 1 0 3x
14 2x 1 0 5x 13 0
5x 13
x 13 / 5
3
In the circuit below, if all the resistors are
identical, what is the voltage drop across
resistor R2?
Same current as R1 and same resistance
?V ?V
?right loop ?V - ?V 0
?V
?V
R1
R2
?V ?
? 8 V
How do the currents compare here and here?
Loop rule (bottom left loop)
Give me an expression that describes the current
I1 through R1
4
In the circuit below all the resistors are
identical.
Same current as R1 and same resistance
?V ?V
?right loop ?V - ?V 0
?V
I1 2I2
?V
R1
R2
?V ?
? 8 V
Both same current, I2
Loop rule (bottom left loop)
What equation best describes the CW full
outermost loop?

• 8v I2R1 I2R - I2R2 0
• -8v I2R1 I2R I2R2 0
• -8v 2I2R1 2I2R I2R2 0
• 4) 8v - 2I2R1 - 2I2R - I2R2 0

5
In the circuit below all the resistors are
identical.
Same current as R1 and same resistance
?V ?V
?right loop ?V - ?V 0
?V
I1 2I2
?V
R1
R2
?V ?
? 8 V
Both same current, I2
Loop rule (bottom left loop)
What is the voltage drop across resistor R2?

• 0.2 volts 2) 1.0 volts
• 1.2 volts 4) 1.6 volts
• 5) 2.0 volts 6) 4.0 volts

6
Sample Problem
V1 9 V
I2
R1 25 ?

• Determine the magnitudes and directions of the
  currents through R1 in the figure at right.

2
R2 15 ?
I1
Label Currents
1
I3
Junction Rule
I1 I2 I3
Loop Rule (1)
V2 I1R2 0
V2 6 V
Loop Rule (2)
I1R2 I2R1 V1 0
Solve Loop Rule (1) for I1 Plug into Loop Rule (2)
Algebra
Comments
I2 3/5 Amp What does the minus sign
mean? Current goes in opposite direction of arrow