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DC CIRCUITS AND INSTRUMENTS
Chapter 18 Problems
18-1/18-3
5,6,7,8,9,12,14
18-4
15,17,21,23
18-5
29,31,33
DC CIRCUITS AND INSTRUMENTS
OBJECTIVES
1. Determine the equivalent resistance of resistors arranged in series
or in parallel or the equivalent resistance of a series-parallel
combination.
2. Use Ohm's law and Kirchhoff’ s rules to determine the current
through each resistor and the voltage drop across each resistor in a
single loop or multiloop dc circuit.
3. Distinguish between the emf and the terminal voltage of a battery
and calculate the terminal voltage given the emf internal resistance
of the battery and external resistance in the circuit.
4. Determine the equivalent capacitance of capacitors arranged in
series or in parallel or the equivalent capacitance of a series-parallel
combination.
Objectives
5. Determine the charge on each capacitor and the voltage drop across
each capacitor in a circuit where capacitors are arranged in series,
parallel or a series-parallel combination.
6. Calculate the time constant of a RC circuit. Determine the charge on
the capacitor and the potential difference across the capacitor at a
particular moment of time and the current through the resistor at a
particular moment in time.
7. Describe the basic operation of a galvanometer and calculate the
resistance which must be added to convert a galvanometer into an
ammeter or a voltmeter.
8. Describe how a slide wire potentiometer can be used to determine the
emf of a source of emf.Given the emf of a standard cell, use the slide
wire potentiometer to calculate the emf of the unknown.
9. Describe how a Wheatstone bridge circuit can be used to determine
the resistance of an unknown resistor. Given three known resistors
and a Wheatstone bridge circuit, calculate the resistance
of an unknown resistor.
KEY TERMS AND PHRASES
resistors in series
resistors in parallel
internal resistance
terminal voltage
Kirchhoff s junction rule
Kirchhoff s loop rule
capacitors in series
capacitors in parallel
RC circuit
time constant
galvanometer
ammeter
voltmeter
shunt resistor
slide wire potentiometer
Wheatstone bridge
RESISTORS IN SERIES
 A simple SERIES CIRCUIT is shown in the
diagram below. The current (I) at every
point in a series circuit equals the current
leaving the battery.
I1= I2=I3=ITotal
RESISTORS IN SERIES
 Assuming that the connecting wires offer no resistance to
current flow, the potential difference between the terminals
of the battery (V) equals the sum of the potential
differences across the resistors, i.e.,
V=Vl+ V2+ V3
•The equivalent electrical
resistance (R) for this
combination is equal to the
sum of the individual
resistors, i.e.,
R=R1+ R2+ R3
RESISTORS IN PARALLEL
In a simple PARALLEL CIRCUIT, the current leaving the
battery divides at junction point A in the diagram shown
below and recombines at point B. The battery current (I)
equals the sum of the currents in the branches. In general
I = I1 + I2 + I3
RESISTORS IN PARALLEL
• If no other resistance is present, the potential difference
across each resistor equals the potential difference across
the terminals of the battery.
• The equivalent resistance (R) of a parallel combination
is always less than the smallest of the individual resistors.
The formula for the equivalent resistance is as follows:
•
1/R = 1/RI + 1/R2 + 1/R3
 The potential
difference across each
resistor in the
arrangement is the
same, i. e.

V = VI = V2 = V3
RESISTORS IN PARALLEL
In a simple PARALLEL CIRCUIT, the current leaving the
battery divides at junction point A in the diagram shown
below and recombines at point B. The battery current (I)
equals the sum of the currents in the branches. In general
I = I1 + I2 + I3
EMF AND TERMINAL
VOLTAGE
 All sources of emf have what is known as INTERNAL
RESISTANCE (r) to the flow of electric current. The internal
resistance of a fresh battery is usually small but increases
with use. Thus the voltage across the terminals of a battery is
less than the emf of the battery.
 The TERMINALVOLTAGE (V) is given by the equation
V =  - Ir, where  represents the emf of the source of
potential in volts, I the current leaving the source of emf in
amperes and r the internal resistance in ohms.
 The internal resistance of the source of emf is always
considered to be in a series with the external resistance
present in the electric circuit.
KIRCHHOFF'S RULES
 KIRCHHOFF'S RULES are used in conjunction with
Ohm's law in solving problems involving complex circuits:
 KIRCHHOFF'S FIRST RULE or JUNCTION RULE: The
sum of all currents entering any junction point equals the
sum of all currents leaving the junction point. This rule is
based on the law of conservation of electric charge.
 KIRCHHOFF'S SECOND RULE or LOOP RULE: The
algebraic sum of all the gains and losses of potential
around any closed path must equal zero. This law is based
on the law of conservation of energy.
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
1. Place a (+) sign next the long line of the battery symbol
and a (-) sign next to the short line. Start choosing a direction
for conventional current flow ( flow of positive charge )
If you choose the wrong direction for the flow of current in a
particular branch, your final answer for the current in that
branch will be negative. The negative answer indicates that
the current actually flows in the opposite direction.
I
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
 2. Assign a direction to the circuit in each independent
branch of the circuit. Place a positive sign on the side of
each resistor where the current enters and a negative sign
on the side where the current exits, e.g.; This indicates that
a drop in potential occurs as the current passes through the
resistor .
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
 Notice how the
directions of the
currents are labeled
in each branch of
the circuit
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
 3. Select a JUNCTION POINT and apply the
junction rule, e.g., at point A in the diagram:
The junction rule may be applied at more than one
junction point. In general, apply the junction rule
to enough junctions so that each branch current
appears in at least one equation.
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
 4. Apply Kirchhoff’s loop rule by first taking note
whether there is a gain or loss of potential at each resistor
and source of emf as you trace the closed loop. Remember
that the sum of the gains and losses of potential must add
to zero.
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
For example, for the left loop of
the sample circuit above start
at point B and travel
clockwise around the loop.
Because the direction chosen
for the loop is also the
direction assigned for the
current, there is a gain in
potential across the battery
(- to +), but a loss of
potential across each resistor
(+ to -).
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
 Following the path of the
current shown in the
diagram and using the
loop rule, the following
equation can be written:
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
The direction taken around the
loop is ARBITRARY. Tracing
a counterclockwise path around
the circuit starting at B, as
shown in the above right
diagram, there is gain in
potential across each resistor
to (- to +) and a drop in
potential across the battery (+
to -). The loop equation would
then be:
SUGGESTIONS FOR USING KIRCHHOFF'S
LAWS
 Multiplying both sides of the above equation by - 1 and
algebraically rearranging, it can be shown that the two
equations are equivalent. Be sure to apply the loop rule to
enough closed loops so that each branch current appears in
at least one loop equation. Solve for each branch current
using standard algebraic methods.
“Solve
simultaneous
equations”
CAPACITORS IN SERIES AND
PARALLEL
 A circuit with
CAPACITORS IN
PARALLEL is shown in the
diagram below. According to
Kirchhoff ‘s loop rule, the
potential difference (V) of the
source of emf:

V = VI = V2 = V3
CAPACITORS IN PARALLEL
 The total charge stored on the capacitor plates (Q) equals




the amount of charge which left the source of:
Q = Ql + Q2 + Q3 ( Charge is additive)
and since Q = CV then
CV = CV1 + CV2 + CV3
C= C1+ C2 +C3 (Capacitance is additive)
CAPACITORS IN SERIES
 For CAPACITORS IN
SERIES, the amount of charge
(Q) that leaves the source of
emf equals the amount of
charge that forms on each
capacitor:
 Q = Ql = Q2 = Q3
CAPACITORS IN SERIES

From Kirchhoffs loop
rule, the potential
difference across the
source of emf (V) equals
the sum of the potential
differences across the
individual capacitors:
Circuits containing resistors and
capacitors
An RC CIRCUIT consists of a resistor and a capacitor
connected in series to a de power source.When switch
1 (S1), shown in the diagram below, is closed, the
current will begin to flow from the source of emf and
charge will begin to accumulate on the capacitor.
Using Kirchhoff s loop rule it can be shown that