How does this current compare with the current for the series circuit? It's more. This is sensible. Connecting resistors in parallel provides alternative pathways and makes it easier for current to flow. How much current flows through each resistor? Because they have equal values, the current divides, with 6 mA flowing through R1, and 6 mA through R2.

To complete the picture, the voltage across R1 can be calculated as:

This is the same as the power supply voltage. The top end of R1 is connected to the positive terminal of the battery, while the bottom end of R1 is connected to the negative terminal of the battery. With no other components in the way, it follows that the voltage across R1 must be 6 V. What is the voltage across R2? By the same reasoning, this is also 6 V.

Here is a slightly more complex circuit, with both series and parallel parts:

Circuit with series and parallel resistors

To find the overall resistance, the first step is to calculate the resistance of the parallel elements. You already know that the combined resistance of two 1 resistors in parallel is 0.5 , so the total resistance in the circuit is 1+0.5=1.5 . The power supply current is:

This is the current which flows through R1. How much current will flow through R2? Since there are two equally easy pathways, 2 mA will flow through R2, and 2 mA through R3.

The voltage across R1 is given by:

This leaves 2 V across R2 and R3, as confirmed by the calculation for R2:

Again, the sum of the voltages around the circuit is equal to the power supply voltage.

Check through this section carefully. A clear understanding of the concepts involved will help tremendously.

Power rating

When current flows through a resistance, electrical energy is converted into heat. This is obvious in an electric torch where the lamp filament heats up and glows white hot. Although the result may be less evident or imperceptible, exactly the same process of energy conversion goes on when current flows through any electronic component.

The power output of a lamp, resistor, or other component, is defined as the rate of change of electrical energy to heat, light, or some other form of energy. Power is measured in watts, W, or milliwatts, mW, and can be calculated from:

where P is power.

What is the power output of a resistor when the voltage across it is 6 V, and the current flowing through it is 100 mA?

0.6 W of heat are generated in this resistor. To prevent overheating, it must be possible for heat to be lost, or dissipated, to the surroundings at the same rate.

A resistor's ability to lose heat depends to a large extent upon its surface area. A small resistor with a limited surface area cannot dissipate (=lose) heat quickly and is likely to overheat if large currents are passed. Larger resistors dissipate heat more effectively.

Look at the diagram below which shows resistors of different sizes:

The standard size of carbon film resistor used in most circuits has a power rating of 0.5 W. This means that a resistor of this size can lose heat at a maximum rate of 0.5 W. In the example above, the calculated rate of heat loss was 0.6 W, so that a resistor with a higher power rating, 1 W or 2 W, would be needed. Some resistors are designed to pass very large currents and are cased in aluminium with fins to increase surface area and promote heat loss.

Input and signal processing subsystems in electronic circuits rarely involve large currents, but power rating should be considered when circuits drive output transducers, such as lamps, LEDs, and loudspeakers.

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