Series and Parallel Circuits

Series Circuit

• Current must pass through all resistors

Rules for Series1. Total (equivalent) resistance is sum of individual

resistances.

RE=R1+R2+…+Rn

2. Current is the same everywhere in circuit and equals voltage of battery divided by equivalent resistance.

I=V/RE and I1=I2=…=In

3. Voltage drop across each resistor equals current times value of that resistor. Sum of individual voltage drops equals voltage of battery.

Vn=IRn and VE=V1+V2+…+Vn

EXAMPLE

1055ER

AV

I 210

20

Find equivalent resistance:

Find current:

Find voltage drop across each resistor:

VAV 10)5)(2(1

VAV 10)5)(2(2

Parallel Circuits

• Current splits between resistors

Rules for Parallel

1. Total resistance is reciprocal of sum of reciprocals of individual resistances.

1. Total current is voltage of battery divided by total resistance. Current through each resistor is voltage of battery divided by individual resistance. Total current is sum of currents in individual branches.

2. Voltage drop across each resistor equals voltage of battery.

nE RRRR

1...

111

21

nT

nn

IIII

R

VI

...21

nbattery VVVV ...21

EXAMPLE

5.22

5

5

2

5

1

5

11

E

E

R

R

AV

I

AV

I

45

20

45

20

2

1

Find equivalent resistance:

Find current through each resistor:

Check by finding total current:

AV

IT 85.2

20

EXAMPLE 2 (cont’d)Remember voltage drop across each resistor equals voltage of battery because all energy is used up in one resistor that is passed through:

VVV 2021