This document discusses the math for series and parallel circuits. For series circuits, current is constant, total resistance is the sum of individual resistances, and total voltage is the sum of individual voltages. For parallel circuits, voltage is constant, total current is the sum of individual currents, and the reciprocal of total resistance equals the sum of the reciprocals of individual resistances. Sample problems are provided to demonstrate how to calculate current, voltage, resistance, and fill out tables for series and parallel circuits.

1. Circuit Math
Discovery
Lab

2. Series Circuit Math
• Current in series is constant
IS = I1 = I2 = I3 …
• Total Resistance in Series is
sum of all resistances
RS = R1 + R2 + R3 …
• Total Voltage in Series is sum
of all voltages
VS = V1 + V2 + V3 …
VS
(S stands for Series)
V1=IR1
V2=IR2
V3=IR3

3. Sample: Series. Fill in the table.
VS=40 V
321
VS
= 40 V IS
= RS =
V1
= I1
= R1 = 1 Ω
V2
= I2
= R2 = 2 Ω
V3
= I3
= R3 = 3 Ω
1. RS = R1 + R2 + R3
2. VS = I RS
4. V1 = I R1
3. IS = I1 = I2 = I3
6 Ω6.67 A
6.67 A
6.67 A
6.67 A
6.67 V
13.3 V
20.0 V

4. Parallel Circuit Math
• Voltage in parallel is constant
VP = V1 = V2 = V3 …
• Current in parallel is the sum of all
the currents
IP = I1 + I2 + I3 …
• The reciprocal of the total
resistance is equal to the sum of
the reciprocals of the individual
resistances
1 1 1 1
RP = R1 + R2 + R3 + …
VP
1
2
3

5. Sample: Parallel. Fill in the table.
Vp
= 20.0 V Ip
= Rp =
V1
= I1
= R1 = 3 Ω
V2
= I2
= R2 = 2 Ω
V3
= I3
= R3 = 1 Ω
0.545 Ω36.7 A
6.67 A
10.0 A
20.0 A
20.0 V
20.0 V
20.0 V
VP
1
2
3
1. VP = V1 = V2 = V3
2. V = I R
3. IP = I1 + I2 + I3
4. VP = IP RP
Notice that there are
more than 1 way to go
about solving these
problems! This acts as
a great way to double
check yourself!

6. Sample: Parallel. Fill in the table.
Vp
= 20.0 V Ip
= Rp =
V1
= I1
= R1 = 3 Ω
V2
= I2
= R2 = 2 Ω
V3
= I3
= R3 = 1 Ω
0.545 Ω36.7 A
6.67 A
10.0 A
20.0 A
20.0 V
20.0 V
20.0 V
VP
1
2
3
1. VP = V1 = V2 = V3
2. V = I R
3. IP = I1 + I2 + I3
4. VP = IP RP
Notice that there are
more than 1 way to go
about solving these
problems! This acts as
a great way to double
check yourself!