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 = I1 = I2 = I3
V = V1 + V2 + V3
V
I Rt = I1R1 + I2R2 + I3R3
Rt = R 1 + R 2 + R 3
5
Resistor in Parallel
• Resistors in parallel have the same voltage’s magnitude
 V = V 1 = V2 = V3
 It = I 1 + I 2 + I 3
 V/Rt = V/R1 + V/R2 + V/R3
V
 1/Rt = 1/R1 + 1/R2 + 1/R3
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 I1, I2, I3 ?
Solution
Khirchoff 1
Khirchoff 2 : voltage in loop circuit
11
RC CIRCUITS
• A circuit containing a series combination of a resistor and a capacitor 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
circuit after the switch is closed
rule
to
the
• 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
decrease to 1/e of its initial value
• In time  , I  e I  0.368I , while in time 2 , I  e I  0.135I
1
2
0
0
0
0
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
I  dq dt
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