CK-12-Physics-Concepts - Intermediate

19.2. Parallel Circuits http://www.ck12.org

In the design of this parallel circuit, each resistor (light bulb) is connected across the battery as if the other two

resistors were not present. Remember that the current going through each resistor goes through only the one resistor.

Therefore, the voltage drop across each resistor must be equal to the total voltage drop though the circuit.

VT=V 1 =V 2 =V 3

The total current passing through the circuit will be the sum of the individual currents passing through each resistor.

IT=I 1 +I 2 +I 3

If we return to the analogy of a river, a parallel circuit is the same as the river breaking into three streams, which

later rejoin to one river again. The amount of water flowing in the river is equal to the sum of the amounts of water

flowing in the individual streams.

Ohm’s Law applies to resistors in parallel, just as it did to resistors in a series. The current flowing through each

resistor is equal to the total voltage drop divided by the resistance in that resistor.

I 1 =

VT

R 1

and I 2 =

VT

R 2

and I 3 =

VT

R 3

SinceIT=I 1 +I 2 +I 3 ,

thenIT=VRT 1 +VRT 2 +VRT 3 ,

andVRTT=VRT 1 +VRT 2 +VRT 3.

If we divide both sides of the final equation byVT, we get the relationship between the total resistance of the

circuit and the individual parallel resistances in the circuit. The total resistance is sometimes called theequivalent

resistance.

1

RT

=

1

R 1

+

1

R 2

+

1

R 3

Consider the parallel circuit sketched below.

The voltage drop for the entire circuit is 90. V. Therefore, the voltage drop in each of the resistors is also 90. V.