This document discusses equivalent resistance in simple series and parallel circuits. It explains that in a series circuit, the total resistance is found by adding the individual resistances together. In a parallel circuit, the total resistance is calculated by taking the inverse of the sum of the inverses of the individual resistances. The document provides examples of calculating equivalent resistance, current, and voltage in various simple series and parallel circuit configurations.

1. Simple Circuits
Equivalent resistance  If you
replaced all the resistors in the
circuit with one resistor, then how
many ohms would it have?

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