Electrical theory 1.2c - how to calculate parallel circuits

In this section I'll explain how to calculate various electrical values for parallel circuits for DC (AC is different and of little interest to us).

Parallel circuit

Here's a parallel circuit made of resistors and a DMM supplied from a bridge rectifier/ transformer. (For this topic we'll ignore the bridge rectifier/ transformer.)

Note: In a parallel circuit, more than one current flows in the whole circuit. The very important point is the voltage across each parallel path is the SAME!

Important points:

1. Light bulbs, resistors, relay coil & contact, and mechanical switches are calculated on resistance;
2. batteries, transformer/ bridge rectifier, switching power supplies are calculated on voltage;
3. electronic components, eg LED are calculated primarily on voltage dropped across them;
4. the above is satisfactory for simple lighting circuits using DC.

HINT:
When doing parallel calculations, the supply voltage is applied to each current path/ branch and Ohm's Law is repeatedly used to give each current.

Calculate Current values

Let's assume the DMM voltmeter (V) measures 10.0V dc which is applied to each branch.

DMM current

The resistance of DMM is 1MΩ which is short hand for 1,000,000 Ohms. Using Ohm's Law,

current (IDMM) = voltage/ Rm = 10/ 1,000,000 = 0.000010A

330Ω resistor current

again,                            I330= V/ R1 = 10/ 330 = 0.030303A

1kΩ resistor current
The resistance is 1kΩ which is short hand for 1,000 Ohms. Using Ohm's Law,

again,                             I1k = V/ R2= 10/ 1,000 = 0.010A

Total current

The individual branch currents are shown on the diagram above. At the rectifier terminal, the total current equals the sum of all branch currents.

So              total current =  IDMM  + I330 +  I1k
                                      =   0.000010A + 0.030303A  + 0.010A = 0.040313A

Alternative calculation method for resistor branches only

In practical terms we can ignore the DMM because its resistance is very much greater than other resistors.

So we can use the parallel resistor equation to get a total resistance value which must be less than either resistor values because there's 2 branches.

R total =    R1 * R2
                (R1 + R2)

so putting in values              R total =    330 * 1000          = 248Ω
                                                             (330 + 1000)

so total current                        I = V/ R total  = 10/ 248    = 0.040303A

This total current approximates the exacting total current value calculated before.

For lighting, this is all you need to know about calculations for parallel circuits.

However, here's some important points on paralleling components:

• batteries: connected in parallel means the output voltage equals one battery voltage. However, the maximum current output capability is summed by all batteries;

• LEDs have individual voltage drops according to the colour of light emitted - see LEDs. You can't connect LEDs of different colours directly in parallel - the lowest voltage drop LED will stop other LED(s) turning on;

• You can't connect diodes in parallel to increase current capability - use a higher rated diode.

NEXT >> Series Parallel circuits