Kirchhoff’s Rules
1) Junction Rule:
The sum of currents entering a junction is equal to the sum of
currents leaving it (conservation of charge and current).
2) Loop Rule:
Around any closed loop, the sum of potential changes is equal
to zero (conservation of energy).
The potential decreases when you go with the flow of current
through a resistor.
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20.79: Wheatstone Bridge
Find potential difference between
B and D
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20.109
I3 = 0.5 A
I1
Given that the current
in the 8 ! resistor is
0.5 A:
I
(a) How much current
is supplied by the
battery?
(b) What is the current
in the 9 ! resistor?
B
A
I1 = I3+I4
D
I4
C
I2
I5
I2 = I5+I6
I = I1 + I2
I6
I=?
I5 = ?
V
I
I = I1+I2
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A galvanometer
Full scale deflection (fsd) = 0.1 mA
(for example)
Meter
Rc
Resistance of galvanometer coil
A torque is exerted on the coil when a current
flows through it. The rotation of the coil is resisted
by a spring. The angle of rotation is proportional
to the current in the coil.
41
Mode of operation of an ammeter to measure current
The ammeter is inserted into the
circuit to measure the current
flowing around the circuit.
Ideally, the ammeter should have
negligible resistance so as not to
affect the current being measured.
R
42
Measurement of current
Ammeter – a bypass (shunt) resistor is placed in
parallel with a galvanometer to limit the current
through the galvanometer to no more than that for
full scale deflection (fsd)
To measure 60 mA when the fsd is 0.1 mA:
VAB = 0.1RC = 59.9R (mV)
galvanometer
(fsd)
So, for the shunt resistor:
0.1
R = RC
= 0.00167RC
59.9
To measure current I: R = RC
fsd
I − fsd
20.83
43
Prob. 20.83: A galvanometer has a coil resistance of 12 ! and a full
scale deflection current of 0.15 mA. It is used with a shunt resistor to
make an ammeter that registers 4 mA at full scale deflection.
Find the equivalent resistance of the ammeter.
• Work out what is the potential difference across the galvanometer
when 0.15 mA flows through it.
• Find what the shunt resistance needs to be to produce an equal
potential difference when the current flowing through the shunt resistor
is 4 – 0.15 mA.
44
Mode of operation of an voltmeter to measure voltage
The voltmeter is attached to two points
of a circuit between which the potential
difference is to be measured.
Ideally, the voltmeter should have very
large resistance so as to draw very little
current from the circuit being studied.
45
Measurement of voltage
Coil resistance
galvanometer
I f sd = 0.1 mA
A resistor (not shown) is put in series
with the galvanometer to limit the
current flowing through the
galvanometer to that giving full scale
deflection (fsd) at the desired
voltage.
To measure 100 V when fsd is at 0.1 mA and the coil resistance RC = 50 !:
(R = resistance put in series with the galvanometer
to convert it to a voltmeter)
V
100 V
That is, R =
− RC =
− (50 !) = 999, 950 !
I f sd
0.1 × 10−3 A
V = I f sd (R + RC )
R ! 1 M!
20.82
46
Prob. 20.82: Voltmeter A has an equivalent resistance of 2.4 " 105 ! and
a full scale voltage of 50 V.
Voltmeter B uses the same galvanometer. It has an equivalent resistance
of 1.44 " 105 !. What is its full scale voltage?
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Prob. 20.85: Consider a circuit consisting of two 1550 ! resistors
connected in series across a 60 V battery.
a) Find the voltage across one of the resistors.
b) A voltmeter has a fsd voltage of 60 V and uses a galvanometer with a
full scale current of 5 mA.
Determine the voltage this voltmeter registers when it is connected
across the resistor in part a).
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