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Electricity

Series Circuits

Calculation of Voltages and Current in a Series Circuit.

If the supply voltage (from the cell) is 12 volts
in the circuit below,
what are the voltages across each resistor?

From the previous page, the total resistance is 9 ohms.

In a series circuit the current is the same everywhere.

The equation
voltage = current x resistance   V = I x R

can be rearranged to give
current = voltage ÷ resistance    I = V ÷ R

In the circuit above,
I = V ÷ R
= 12 ÷ 9
= 1·333 amps.
Compare this current with a parallel circuit.

Using the same equation V = I x R for each resistor in turn
(and rounding up numbers) gives

V1 = 1·333 x 2
= 2·667 volts.

V2 = 1·333 x 3
= 4·000 volts.

V3 = 1·333 x 4
= 5·333 volts.

We can see that the largest resistor at 4 ohms
has the largest voltage (5·333 volts)
and the smallest resistor at 2 ohms has the
smallest voltage (2·667 volts) across it.

In energy terms, the largest amount of work is done
by the charge moving through the largest resistance.

Finally, we can check that the voltage across
all of the components adds up to the supply voltage.

V1 + V2 + V3 = 2·667 + 4·000 + 5·333

= 12 volts.

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