Chapter 18 Direct Current CIRcuits

18.1 Sources of emf (Electromotive Force)

• The source that maintains the constant current in a closed circuit is called a source of emf, i.e. batteries and generators.

• A battery (Figures 18.1)

• The maximum potential difference is called the electromotive force (emf, E) of the battery.

• In reality, batteries have a small resistance to be added to the circuit. This resistance is called the internal resistance of the battery.

• The internal resistance causes the voltage between the terminals to drop below the maximum value specified by the battery’s emf. The actual voltage between the terminals of a battery is know as the terminal voltage ()

= E -

• Examples.

18.2 Resistors in Series

• When the devices are wired in series (serial wiring), the same electric current is flowing through each device.

• Figure 18.2

• V = V₁ + V₂ + … ; I₁ = I₂ = …

• The equivalent resistance (R_s) is

R_s = R₁ + R₂ + …

• Examples

18.3 Resistors in Parallel

• When the devices are wired in parallel (parallel wiring), the same voltage is applied across each device.

• Figure 20.19 and 20.21

• I = I₁ + I₂ + … ; V₁ = V₂ = …

• The equivalent resistance (R_s) is

1/R_p = 1/R₁ + 1/R₂ + …

• Examples

18.4 Kirchhoff’s Rules and Complex DC Circuits (Skip)

18.5 RC Circuits

• Figure 18.13 (a resistor-capacitor circuit)

• Assuming that the capacitor is uncharged at time t = 0 when the switch is closed, the magnitude q of the charge on the capacitor at time t is

q = Q [1 – e^-t/RC] (20-20)

where Q = C E and the exponential e has the value of 2.718.

• The term RC in the exponent is called the time constant t of the circuit:

t = RC

The time constant is the amount of time required for the capacitor to accumulate 63.2 % of its equilibrium charge. The charge approaches its equilibrium value rapidly when the time constant is small and slowly when the time constant is large.

• Assuming that the capacitor is fully charged (Q) at time t = 0 when the switch is closed, then the charged capacitor begins discharging. The magnitude q of the remaining charge on the capacitor at time t is

q = Q e^-t/RC (20-22)

• At t = RC, the magnitude of the charge remaining on each plate is Q (0.368). Hence, the time constant is the amount of time required for a charged capacitor to lose 63.2% if its charge.