# Series Circuits

## Voltage and current

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In series circuits the sum of voltages is equal to the applied voltage and can be expressed as

V = V_{1}+ V_{2}+ ... + V_{n}(1)

where

V = applied voltage from the battery or source (volts, V)

V_{1..n}= voltage each resistor (volts, V)

From Ohms Law

V_{n}= I_{n}R_{n}(2)

where

I_{n}= current (amps, A)

R_{n}= resistance (ohms, Ω)

Since in a series circuit

I_{1}= I_{2}= .. = I_{n}(3)

equation (1) can be modified to

R = R_{1}+ R_{2}+ .. + R_{n}(4)

where

R = total circuit resistance (ohms, Ω)

### Example - Series Circuit

For a 12 V car battery series circuit with three resistors *1.25 Ω, 0.5 Ω *and *1.5 Ω, *the total resistance can be calculated as

R = (1.0 Ω) + (0.5 Ω)+ (1.5 Ω)

= 3 Ω

The series circuit current can be calculated as

I = V / R

= 12 / 3

= 4 amps

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