Internal resistance of battery

1
Internal resistance of battery

• Some of the electrical energy is dissipated by
  Joule heating inside the battery.

?e.m.f. across the - terminal of the battery
is lower than the marked value when connected to
external components.
Terminal voltage V
? the voltage across the terminal of a cell is
called the terminal voltage and is usually less
than the e.m.f. of the cell.
2
Finding the internal resistance of the battery

• The current I through the circuit is varied by a
  resistance box which has known value of
  resistance R.

R
? V I r
I R I r
? by plotting a graph of R against 1 / I, a
straight line can be obtained. The slope of the
graph is ? and the intercept on the y-axis is the
internal resistance r.
3
Combination of Resistors

1. In series

All the resistors carry same current I
V V1 V2 V3
I R1 I R2 I R3
I ( R1 R2 R3 )
? R R1 R2 R3
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Combination of resistors
2. In parallel
The p.d. V across each resistors is the same.,
but the current branches into I1, I2 and I3.
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Power and heating effect
The charge pass through the resistor
The electrical energy converted into other form
of energy in ?t
? Power of the resistor
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Example 5 A light bulb labelled 12 V 10W is
connected across a 12 V cell with internal
resistance 5O. Find the power output.
? the cell has internal resistance, the p.d.
across the light bulb ?12 V. But the resistance
of the bulb is fixed.
The total resistance of the circuit is 5O 14.4
O 19.4 O
The current flow through the circuit and the bulb
is 12 V / 19.4 O 0.619 A
7
Classwork 1 A student connect a toy motor
labelled 9 V 50 W across a 9 V battery with
internal resistance 10 O. Find the power
output by the toy motor.
The total resistance of the circuit is 1.62O 10
O 11.62 O
The current flow through the circuit and the toy
motor is 9 V /11.62 O 0.775 A
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Power output and Resistance
The current flow through the above circuit
Power output through R
Max power occurs when R r
9
Proof of max. Power output
10
Efficiency of Electric Circuit
In general the power of the circuit.
When max. power occurs, R r, the efficiency is
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Example 6 A 1.5 V cell has an internal resistance
of 2 O. Find the condition for a.) Max.
Power. b.) Max. Efficiency.
a.) Max. Power consumption occur when the cell
is short circuit.
b.) Max. useful power output occur when R
r i.e. external resistance 2O
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Classwork2 A 9 V cell has an internal resistance
of 5 O. Find the power out put for a.) Max.
Power. b.) Max. Efficiency.
a.) Max. Power consumption occur when the cell
is short circuit.
b.) Max. useful power output occur when R
r i.e. external resistance 5O
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Power transmission
In power transmission, the voltage across the
power cable is VL VL. or ILR, where L is the
current through the cable.
The power loss by the cable is
? Power transfer to the user equal to the power
generate, it usually remains constant
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Typical Example ---- Combination of 2 cells
Since any charge or cannot climb through the
energy barrier set by the other cell, NO current
flow through the cells.
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Example 6 A 12V battery of internal resistance 15
O is recharged by a 14 V d.c. supply with
internal resistance 5O via a 20 O. Find the
current through the battery.
Net e.m.f. 14 V 12 V 2 V
Total resistance 15 5 20 40O
Current 2 V / 40 O 0.05 50 mA
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Classwork3 A student uses a 9V battery of
internal resistance 10 O to charged a 1.5 V
AAbattery with internal resistance 5O via
a 50 O resistor. Find the current through
the battery.
Net e.m.f. 9 V 1.5 V 7.5 V
Total resistance 10 5 50 65O
Current 7.5 V / 65 O 0.115 A
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2 parallel cell connected to a resistor
The terminal voltage of the cells are the same
and equal to the voltage across R
? I1 r1 I R
? I2 r2 I R
I1 I2 I
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Example 6 The light bulb in the diagram shown
below has a resistance of 6 O. Find the power
output.
1.5 V I 6O I1 2O --- ( 1 )
1.5 V I 6O I2 4O --- ( 2 )
I I1 I2 --- ( 3 )
1.5 V (I1 I2 ) 6O I1 2O
1.5 V (I1 I2 ) 6O I2 4O
Solve, I1 0.06818 A and I2 0.136 A i.e. I
0.06818 0.136 0.2042 A
? Power output of the bulb 0.20422 6 0.25 W
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Classwork 4 The light bulb in the diagram shown
below has a resistance of 10 O. Find the
power output.
1.5 V I 10O I1 5O --- ( 1 )
1.5 V I 10O I2 2O --- ( 2 )
( 1 ) 2, ( 2 ) 5
I 0.13125 A
? Power output of the bulb 0.131252 10
0.17226 W
20
I-V characteristics of junction diode (
semiconductor diode )
A diode allow current flow in 1 direction only.
However, the voltage across the diode must reach
a certain value to enable the charge carriers to
flow.
For the diode to operate, I ?20 mA, the largest I
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For a diode to operate safely, prevent it burn
out, a maximum current must be noticed. This
current is limited by the power rating of the
diode.Assume a diode has a maximum rating of
0.08 W, the smallest R is given by
For the diode to operate safely,
? the diode can be operated with a resistor of
22O?R ?110 O
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Classwork 5 The I-V characteristic of a diode is
shown below. The diode is operated with a
resistor R. Given that the maximum power
rating of the diode is 1 W. Calculate the
maximum and minimum value of the resistor.
Rmax 156 O
Rmin 9.36 O
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Thermionic diode ??????
A thermionic diode is a evacuated glass tube with
a heated cathode. Electrons is excited in the
cathode and jump to the anode inside the glass
tube.
If a diode is saturated at I 2 mA, the number
electrons reaches a maximum value and nor more
electrons can flow inside the glass tube.
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If the diode is just saturated, the voltage
across the diode VD is 4 V and the current I 2
mA.
12 V VD I R VD 2 mA R ? VD 12 V - 2
mA R
Since I must be larger than 2 mA, the resistor
must be smaller than a certain value.
VD gt 4V ? 12V 2 mA R gt 4V
? R lt 4000 O
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Bridge circuit
4 V
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VP VR
? I1 P I2 R
VQ VS
? I1 Q I2 S
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Classwork 6 The ammeter in the diagram below
shows no reading. Calculate the resistance of the
unknown resistor P
P 40 O