C H A P T E R   20Electric Circuits

20.10 Kirchhoff's Rules

There are two KIRCHHOFF'S RULES.

1. Junction rule 2. Loop rule

These are useful in circuit analysis.

Kirchhoff's Rules

Junction rule. The sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction.

Loop rule. Around any closed circuit loop, the sum of the potential drops equals the sum of the potential rises.

Junction Rule

Junction rule. The sum of the magnitudes of the currents directed into a junction equals the sum of the magnitudes of the currents directed out of the junction.

Application of Junction Rule

Q: A galvanometer with a full-scale limit of 0.100 mA is to be used to measure a current of 60.0 mA. How much current will pass through the shunt resistance R?

A: 60.0 – 0.1 = 59.9 mA

Loop Rule

Loop rule. Around any closed circuit loop, the sum of the potential drops equals the sum of the potential rises.

Application of Loop Rule

The circuit shown below contains two batteries and two resistors. Determine the current I in the circuit.

Current Measurement

Voltage Measurement

Capacitors in Parallel

Capacitors in Series

RC CIRCUITSCharging

RC CircuitsDischarging

The physics of heart pacemakers

Heart pacemakers, for instance, incorporate RC circuits to control the timing of voltage pulses that are delivered to a malfunctioning heart to regulate its beating cycle.

The physics of safe electrical grounding

The physics of the physiological effects of current

Serious and sometimes fatal injuries can result from electrical shock. The severity of the injury depends on the magnitude of the current and the parts of the body through which the moving charges pass. The amount of current that causes a mild tingling sensation is about 0.001 A. Currents on the order of 0.01−0.02 A can lead to muscle spasms, in which a person “can’t let go” of the object causing the shock. Currents of approximately 0.2 A are potentially fatal because they can make the heart fibrillate, or beat in an uncontrolled manner. Substantially larger currents stop the heart completely. However, since the heart often begins beating normally again after the current ceases, the larger currents can be less dangerous than the smaller currents that cause fibrillation.