Electrical Circuits in Series
Voltage and current in 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
