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Series Circuits

Voltage and current in series circuits

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series circuits

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

U = U1 + U2 + ... + Un                  (1)

where

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

U1..n = voltage over each resistor (volts, V)

From Ohms Law 

Un = In Rn                     (2)

where

In = current (amps, A)

Rn = resistance (ohms, Ω)

Since the currents in a series circuit are equal

I1 = I2 = .. = In                    (3) 

- equation (1) can be modified to

R = R1 + R2 + .. + Rn                 (4)

where

R = total circuit resistance in the circuit (ohms, Ω)

Example - Series Circuit

To a 12 V car battery three resistors 1.25 Ω, 0.5 Ω and 1.5 Ω are connceted in series. The total resistance in the circuit can be calculated as

R = (1.0 Ω) + (0.5 Ω) + (1.5 Ω)

    = 3 Ω

The current in the series circuit can be calculated as

I = U / R

    = 12 / 3

    = 4 amps

The power dissipated in the circuit can be calculated

P = R I2

   = (3 Ω) (4 amps)2

   = 48 watts

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