This article covers practical problems that may occur in a household. It was revised on Aug 25, 2010.

Ohm’s Law

Ohm’s Law states that the voltage is equal to the current times the resistance.

Voltage is electrical pressure, current is the flow of electricity and resistance opposes the flow of electricity.

Pressure is measured in volts.

Current is measured in amperes.

Resistance is measured in ohms.

Power is measured in watts.

Review of formulas used in this article:

Voltage = current * resistance

or

Volts = amperes * watts

Power = voltage * current

or

Watts = volts * amperes

Parallel circuits:

In a parallel circuit:

The voltage is the same in every branch of the circuit.

The total current is the sum of the currents in each branch of the circuit.

Example. I have three rooms. I have one light and one switch controlling that light in each room and the lighting for the three rooms is on one fuse. The circuit consists of all light bulbs and switches in the three rooms. Each room contains one branch of the total circuit. The branch for each room is the wiring for the switch and the light bulb in that room. If there are three rooms, then there are three branches. If a switch goes defective in one room, the light bulbs in the other rooms are not affected. Therefore the branch for each room is in parallel with the branches for the other two rooms.

Any air conditioner should be on a circuit that has no other appliances on it. But in many households the air conditioner shares the circuit with other appliances.

To determine how many lights are on a fuse, remove the fuse and then try to turn on each light. You can do the same for outlets. Remove the fuse and then plug a night-light into each outlet to determine which outlets are on that fuse. If you have circuit breakers, you can turn them off.

Problem 1:

An apartment has four rooms. A 100 watt light bulb is in each ceiling light fixture. There is one light fixture per room. Each light fixture is controlled by it’s own switch. The voltage is 110 volts. How much current is being drawn by the four light bulbs?

Solution:

With respect to the 110 volts at the fuse box, the four light fixtures are wired in parallel. The proof is that there is one electrical path per light bulb. If all light bulbs are on and you turn off one light bulb, the others remain on.

Hence the total current is the sum of the currents through each light bulb.

The power dissipated by a light bulb equals the product of the voltage and current.

Therefore the current through each light bulb is

amperes = watts/voltage = 100 volts/110 watts = 0.909 amperes

There are four light bulbs. The total current is

4 light bulbs * .909 amperes per light bulb = 3.64 amperes

Problem 2:

The following items are on the one fuse

An air conditioner that draws 10 amperes.

A 220 watt coffee maker

A 100 watt light bulb

A 300 watt toast maker

The voltage is 110 volts and the fuse is a 15 ampere fuse. Will the fuse blow?

Solution:

Using the formula amperes = watts/volts:

The toast maker dissipates 300 watts and is provided 110 volts.

300 watts/110 volts = 2.73 amperes

The lamp dissipates 100 watts

100 watts/110 volts = 0.909 amperes

The coffee maker dissipates 220 watts of power

220 watts/110 volts = 2 amperes

The total current is the sum of the individual currents.

10 amperes + 2.73 amperes + .909 amperes + 2 amperes = 15.64 amperes.

The current drawn, when the everything is turned on, is more than the rating of the fuse. Therefore the fuse will blow if everything is turned on.

Problem 3:

An old fashion TV set dissipates 1000 watts.

A computer monitor dissipates 500 watts.

Two lamps dissipate 200 watts.

The voltage is 110 volts.

All three items are connected to the same fuse.

What size fuse should be used?

Solution:

The current drawn by the TV set is

Current = power/volts = 1000 watts/110 volts

The current drawn by the computer monitor is

Current = 500 watts/110 volts

The current drawn by the two lamps is

Current = 200 watts/110 volts

Total current = 1000 watts/110 volts + 500 watts/110 volts + 200 watts/110 volts =

1700 watts/110 volts = 15.45 amperes

Therefore a 20 ampere fuse is needed.

References:

I have a Bachelor of Science in Electrical Engineering

I majored in interior house wiring in a Vocational Technical High School

Introductory Circuit Analysis Third Edition

ISBN 0-675-8559-4

Miller’s Guide to Home Wiring

ISBN 0-07-144551-X