Circuit rules

The voltage loop rule states that the net voltage difference around a loop must equal zero. Any energy gained by electrons as they pass through a battery must be expended as they pass through circuit elements in the loop.

The junction rule states that the net current entering a junction must equal the net current leaving the junction. We define the direction of the current to be the direction of flow of positive charges.

Circuit elements

Symbols for common circuit elements are shown above. A battery symbol has the longer line on the positive terminal and the shorter line on the negative terminal. The lines on a capacitor symbol have equal length. A resistor is depicted using zigzag lines.



Moving from negative to positive through a battery causes positive charge carriers to gain potential, while moving from positive to negative causes them to lose potential.

The script E stands for electromotive force (EMF) and equals the potential difference across the battery for an ideal battery. This assumes there is no internal resistance in the battery.

Moving through a resistor in the direction of the current causes the charges to lose potential.

Sample question

Consider this simple circuit, where R₁ = 1.0 Ω, R₂ = 2.0 Ω and V_b = 12 V. Find I₁, I₂ and I₃.

Energy and Power

We know that power is defined as expenditure of energy over time. We can use this basic understanding to define power in a battery and power expended by a resistor.



First we define change in potential energy in terms of the EMF of the battery. Power is the time derivative of potential energy, which can be written in terms of current and EMF. Power in a battery is the product of the current through the battery and the EMF of the battery.



Similarly, the power dissipated through a resistor is the product of the current through the resistor and the potential across the resistor. Ohm's law allows us to write power in other useful ways.

Recall that the units of power are joules per second, or watts. When you receive a bill from your power company, the units will be kilowatt-hours. This is power x time and so, is equal to the energy you have used.

The power supplied to your home is the voltage available, 120 V for an average household. A typical wall outlet is on a circuit breaker at 15 amps. This protects your house from an overheated circuit, which can cause a fire. A larger outlet may be used for an appliance like a freezer of gas dryer.



Your outlet is protected by a fuse. A fuse is just a thin wire or strip of metal that will melt when a current over a certain value goes through it.

Sample questions

1. A 120-volt line is protected by a 15-amp fuse. Will it operate a 1200-watt hair dryer?

2. At $0.10 per kW-hour, how much would it cost to operate an 800-watt hair dryer for 1/2 hour?