Direct Current & Circuits

Resistors in Series

Equivalent Resistance for Resistors in Series

Voltage is the sum of the voltages across each resistor which will add to the voltage of the emf source.

Current is constant across each resistor.

Example 18-1

A circuit of three resistors connected in series to a 24.0 V battery. The current in the circuit is 0.0320 A. Given that and , find (a) the value of and (b) the potential difference across each resistor.

Resistors in Parallel

Equivalent Resistance for Resistors in Parallel

Voltage over each resistor is the voltage across the emf source.

Current is the sum of the current in each branch to sum to the current in the circuit.

Example 18-2

Consider a circuit with three resistors, , , and , connected in parallel with a 24.0 V battery. Find (a) the total current supplied by the battery and (b) the current through each resistor.

Example 18-3

Two identical light bulbs are connected to a battery, either in series or in parallel. Are the bulbs in series (a) brighter, (b) dimmer, or (c) the same brightness as the bulbs in parallel?

Example 18-4

In the circuit shown in the diagram, the emf of the battery is 12.0 V, and all the resistors have a resistance of . Find the current supplied by the battery to this circuit.

R-C Circuits

After each interval of time equal to RC, the curve of Q versus t drops to 36.7879% of the previous value.

The voltage also decays exponentially. The smaller the RC is, the faster the curves decay.

As the charge on the capacitor builds up the current in the circuit dies away.

The equation for an R-C Circuit charge as the capacitor decays.

Example 18-5

A circuit consists of a resistor, a resistor, a capacitor, a switch, and a 3.00 V battery all connected in series. Initially the capacitor is uncharged and the switch is open. At time t = 0 the switch is closed. (a) What charge will the capacitor have a long time after the switch is closed? (b) At what time will the charge on the capacitor be 80% of the value found in part (a)?

Network Analysis

Kirchoff's Rules

The Loop Rule – The algebraic sum of the voltage rises and drops encountered in going around any closed path formed by any portion of a circuit must be zero.

The Node Rule (Junction Rule) – The sum of all the currents entering any node in a circuit must equal the sum of all the currents leaving that node.

Example 18-6

Find the currents , , and in the circuit shown in the figure.

Example 18-7

(a) Under steady-state conditions, find the unkown currents , , and in the multiloop circuit shown in the figure.
(b) What is the charge on the capacitor?

The End