2. Simple
Series
9 V
R1 = 5 Ω R2 = 7 Ω
V = 9 V
Rs = 5 + 7 = 12 Ω
I = 0.75 A
V = I R
9 = I (12)
I = 0.75 A
I = 0.75 A I = 0.75 A
V = 3.75 V V = 5.25 V
• Resistors in series
add up.
• Find the total
current. (V= IR)
• In a series circuit,
the currents are
constant.
• Find the voltages.
(V=IR)
• Double check
yourself In series,
the voltages add up.
3.75
+ 5.25
9
3. Simple
Parallel
9 V
R1 = 4 Ω
R2 = 12 Ω
V = 9 V
1/Rp = 1/4 + 1/12
Rp = 3 Ω
I = 3 A
V = I R
9 = I (3)
I = 3 A
I = 2.25 A
I = 0.75 A
V = 9 V
V = 9 V
• Resistors in parallel
are 1/R = 1/R + 1/R.
• Find the total
current. (V= IR)
• In a parellel circuit,
the voltages are
constant.
• Find the currents.
(V=IR)
• Double check
yourself In
parallel circuit, the
currents add up.
2.25
+ 0.75
3
4. 12 V
12 V
R = 4 Ω
R = 5 Ω
R = 6 Ω
1/Rp = 1/5 + 1/6
Rp = 2.73 ΩR = 4 Ω
Rs = 4 + 2.73
= 6.73 Ω
12 V
I = 1.78 A
I = 1.78 A I = 1.78 A
V = 7.12 V V = 4.86 V
V = 4.86 V
V = 4.86 V
I = 0.81 A
I = 0.96 A
7.12
+4.86
12
Current is
equal in
series.
0.96
+0.81
1.78
Voltages
are equal in
parallel.
Voltages
add up.
Currents add up.
Combine
these two
first into 1
resistor!
5. R1 = 2 Ω R2 = 4 Ω
I = 1.76 A I = 1.76 A
V = 2.11 V V = 3.85 V
V = 6 V
Rs = 1.2 + 2.2 = 3.4 Ω
I = 1.76 A
1/Rp = 1/2 + 1/3
Rp = 1.2 Ω
R2 = 5 ΩR2 = 3 Ω
1/Rp = 1/4 + 1/5
Rp = 2.2 Ω
V = 6 V
V = 6 V
V = 2.11 V
V = 3.85 V
I = 0.77 A
I = 1.06 A
V = 3.85 V
I = 0.96 A
V = 2.11 V
I = 0.70 A
6. 120 V
120 V
72 Ω
120 V
I = 1.78 A
I = 1.6 A I = 1.6 A
V = 115 V V = 4.32 V
4 Ω
27 Ω
3 Ω
72 Ω
4 Ω
1/Rp = 1/27 + 1/3
Rp = 2.7 Ω
4 Ω
Rs = 72 + 2.7
= 74.7 Ω
1/Rp = 1/74.7 + 1/4
Rp = 3.8 Ω
V = 120 V
V = 120 V
I = 1.6 A
I = 30 A
V = 120 V
V = 120 V
I = 1.6 A
I = 30 A
7. 120 V
120 V
72 Ω
120 V
I = 1.78 A
I = 1.6 A I = 1.6 A
V = 115 V V = 4.32 V
4 Ω
27 Ω
3 Ω
72 Ω
4 Ω
1/Rp = 1/27 + 1/3
Rp = 2.7 Ω
4 Ω
Rs = 72 + 2.7
= 74.7 Ω
1/Rp = 1/74.7 + 1/4
Rp = 3.8 Ω
V = 120 V
V = 120 V
I = 1.6 A
I = 30 A
V = 120 V
V = 120 V
I = 1.6 A
I = 30 A
