1. (b) ρ L R = A 1.59 x 10-8 (1.8) (a) (c) (d) (1) GIVEN 0.993 = A
V = 4.50 V
L = 180 cm = 1.8 m
ρ = 1.59 x 10-8 Ωm
I = 4.53 A
(b)
ρ L
R = A
1.59 x 10-8 (1.8)
0.993 = A
A = 2.9 x 10-8 m2
(a)
V = IR
(c)
A = πr2
4.5 = 4.53(R)
2.9 x 10-8 = πr2
R = Ω
r = 9.6 x 10-5 m
d = 1.92 x 10-4 m
(d)
Don’t start all over; 45 cm is ¼ of 180 cm ∴ R will ¼ of 0.99 Ω or Ω

2. (2) VT = IT RT 120 = I (21.4) RT = 5 + 1.2 + 10 + 4 + 1.2 = 21.4 Ω
3 Ω 5Ω
10 Ω
1.2
2 Ω
4 Ω
120 V
4 Ω
2 Ω
6 Ω 12
1.2
6 Ω
VT = IT RT
120 = I (21.4)
RT = = 21.4 Ω
IT = 5.6 amps
This is the current for each single resistor and each group

3. 5Ω 3Ω 2Ω
10Ω 4Ω 6Ω
I = 5.6 amps
V = 28 V
P = 157 watts
I = 5.6 amps
V = 56 V
P = watts
I = 5.6 amps
V = 22.4 V
P = watts

4. V= I R V = 5.6(1.2) V = 6.7 V V3= I3R3 6.7 = I3(3) I3 = 2.23 amps
3 Ω
V = 5.6(1.2)
1.2
V = 6.7 V
2 Ω
This is the voltage for each resistor
V3= I3R3
6.7 = I3(3)
I3 = 2.23 amps
V2= I2R2
6.7 = I2(2)
I2 = 3.35 amps

5. 5Ω 3Ω 2Ω
10Ω 4Ω 6Ω
I = 5.6 amps
V = 28 V
P = 157 watts
I = 2.23 amps
V = 6.7 V
P = 14.9 watts
I = 3.35 amps
V = 6.7 V
P = 22.4 watts
I = 5.6 amps
V = 56 V
P = watts
I = 5.6 amps
V = 22.4 V
P = watts

6. V6= I6R6 V6 = (.56)(6) V6 = 3.36 V V= I R V = 5.6(1.2) V = 6.7 V
4 Ω
V6 = 3.36 V
2 Ω
6 Ω 12
1.2
6 Ω
V= I R
V = 5.6(1.2)
This is voltage for the 2Ω and 4Ω resistors and the 12Ω group
V = 6.7 V
V4= I4R4
6.7 = I3(4)
V= I R
6.7 = I(12)
I4 = 1.68 amps
This is the current for each 6Ω resistor
I = 0.56 amps
V2= I2R2
6.7 = I2(2)
I2 = 3.35 amps

7. 5Ω 3Ω 2Ω
10Ω 4Ω 6Ω
I = 5.6 amps
V = 28 V
P = 157 watts
I = 2.23 amps
V = 6.7 V
P = 14.9 watts
I = 3.35 amps
V = 6.7 V
P = 22.4 watts
I = 5.6 amps
V = 56 V
P = watts
I = 5.6 amps
V = 22.4 V
P = watts
I = 0.56 amps
V = 3.36 V
P = 1.9 watts
I = 0.56 amps
V = 3.36 V
P = 1.9 watts
I = 3.35 amps
V = 6.7 V
P = 22.4 watts
I = 1.68 amps
V = 6.7 V
P = 11.3 watts

8. (a) (3) 1 1 1 = + RT 14 22 RT = 8.55 Ω VT = IT RT 25 = I (8.55)
Before switch is closed = + RT 14 22
RT = 8.55 Ω
12 Ω
4 Ω
VT = IT RT 14 22
25 = I (8.55)
25 V
10 Ω
10 Ω
IT = 2.92 amps
R1 and R2 are in series; R3 and R4 are in series
Both series groups are in parallel
V14= I14R14
Each parallel group gets a voltage of 25 V
V22= I22R22
25 = I14(14)
25 = I22(22)
I14 = 1.78 amps
I22 = 1.14 amps
R1 and R2
R3 and R4

9. (b) 1 1 1
After switch is closed = + R 4 12
R = 3 Ω
12 Ω
4 Ω 3 1 1 1 = +
10 Ω
10 Ω R 10 10 5
R = 5 Ω
R1 and R3 are in parallel; R2 and R4 are in parallel
Both parallel groups are in series
RT = 8 Ω
VT = IT RT
Each group gets a current of amps
25 = I (8)
IT = amps

10. (b) V= IR V= IR V = (3.125)(3) V = (3.125)(5) V = 9.375 V V = 15.625 V
Solve for the I for each resistor
V= IR
V= IR
V = (3.125)(3)
V = (3.125)(5)
V = V
V = V
This is the voltage for R2 and R4
This is the voltage for R1and R3
V= IR
V= IR
V= IR
9.375 = I(12)
= I(10)
9.375 = I(4)
I = amps
I = 0.78 amps
I = 2.34 amps R3 R1
R2 and R4

11. (c)
After switch is closed
Before switch is closed
7.12 V
13.68 V
4 Ω
12 Ω V
4 Ω
12 Ω V
1.14
amps
1.78
amps
10 Ω
10 Ω
10 Ω
10 Ω
Left branch drops 7.12 V while right branch drops V
Do the same thing
Difference in potential between the left and right branches is 6.56 V
V = 0 V after closed

12. (d) I = 2.34 amps through R1 I = 1.56 amps through R2
After switch is closed
(d)
I = 2.34 amps through R1
and
I = 1.56 amps through R2
Thus 2.34 – 1.56 amps flows from a to b
0.781 amps from a to b