DirectCurrentCircuits Electromotive Force Resistors in Series and in

Direct�Current�Circuits • Electromotive Force • Resistors in Series and in Parallel • Kirchhoff ’s Rules • RC Circuits • Electrical Instruments • Household Wiring and Electrical Safety

Electromotive Force • A device that produces an electric field and thu s may cause charges to move around a circuit • Example: a battery or generator • In Fig 1, the potential difference of resistor is equal to emf of the battery • However real battery has always internal resistance r (Fig 2), thus the terminal voltage reduces to • Note that � emf is equivalent to the opencircuit voltage • What is the voltage in the battery’s label ? ?

Electromotive Force (2) • There are voltage drop through r and R • The voltage equation of the circuit is • The flowing current is • The power balance in the circuit

Matching the Load

Resistor in Serial • Resistors connected in serial have the same flowing current I = I 1 = I 2 = I 3 V = V 1 + V 2 + V 3 V I R t = I 1 R 1 + I 2 R 2 + I 3 R 3 Rt = R 1 + R 2 + R 3 5

Resistor in Parallel • Resistors in parallel have the same voltage’s magnitude § V = V 1 = V 2 = V 3 § It = I 1 + I 2 + I 3 § V/Rt = V/R 1 + V/R 2 + V/R 3 V § 1/Rt = 1/R 1 + 1/R 2 + 1/R 3 6

Calculate Equivalent R

KIRCHHOFF’S RULES • In analyzing complex circuit (more than single loop), we need kirchhoff’s rules. • The principles are: 1. The sum of the currents entering any junction in a circuit must equal the sum of the currents leaving that junction: 2. The sum of the potential differences across all elements around any closed circuit loop must be zero:

First Rules

Second Rules

Example Substitute equation (1) into (2) Equation (3) devide by 2 : Find I 1, I 2, I 3 ? Solution Khirchoff 1 Khirchoff 2 : voltage in loop circuit 11

RC CIRCUITS • A circuit containing a series combination of a resistor and a ca -pacitor is called an RC circuit. • Normally, we analyzes the system during steady-state. • Now, we will analyze the circuit prior to steady-state i. e. transient state

Charging Capacitor • The capacitor is initially uncharged • There is no current while switch S is open (Fig. b) • If the switch is closed at t= 0 (Fig. c) the charge begins to flow, setting up a current in the circ uit, and the capacitor begins to charge • Note that during charging, charges do not jump across the capacitor plates because the gap between the plates represents an open circuit • The charge is transferred between each plate and its connecting wire due to E by the battery • As the plates become charged, the potential difference across the capacitor increases • Once the maximum charged is reached, the current in the circuit is zero

Charging Capacitor (2) • Apply Kirchhoff’s loop rule to the circuit after the switch is closed • Note that q and I are instantaneous values that depend on time • At the instant the switch is closed (t = 0) the charge on the capacitor is zero. The initial current • At this time, the potential difference from the battery terminals appears entirely across the resistor • When the charge of capacitor is maximum Q, The charge stop flowing and the current stop flowing as well. The V battery appears entirely across the capacitor

Charging Capacitor (3) • The current is equation , substitute to voltage • Integrating this expression • we can write this expression as

Charging Capacitor (4) • The current is • The quantity RC is called the time constant • It represents the time it takes the current to d ecrease to 1/e of its initial value • In time , while in time

Discharging a Capacitor • The circuit consists of a capacitor with initial charge Q, a resistor, and a switch • When the switch is open (Fig. a), the potential difference Q /C exists across the capacitor • There is zero potential difference across the resistor • If the switch is closed at t = 0 (Fig. b) the capacitor begins to discharge through the resistor • As a result, the current will flow and the charge in the capacitor will be reduced

Discharging a Capacitor (2) • The equation for the circuit is • Substitute into this expression • Integrating this expression • The current is

ELECTRICAL INSTRUMENTS • The Ammeter Ideally, an ammeter should have zero resistance , Why? • Voltmeter An ideal voltmeter has infinite resistance, Why?

HOUSEHOLD WIRING AND ELECTRICAL SAFETY • Utility distributes the power via a pair of wires (live and neutral wire) • Each house is connected in parallel to this line • A meter is connected in series with the live wire entering the house to record the household’s usage of electricity • After the meter, the wire splits so that there are several separate circuits in parallel distributed throughout the house • Each circuit contains a circuit breaker • The wire and circuit breaker for each circuit are carefully selected to meet the current demands