ACTIVITY 13

ACTIVITY 6
AIM
To study the variation in potential drop with length of a wire for a
steady current.

APPARATUS AND MATERIAL REQUIRED

Potentiometer, battery eliminator of constant voltage, dc power
supply or lead accumulator, voltmeter and ammeter of suitable
range, plug key, jockey, rheostat, connecting wires, etc.

P RINCIPLE
If a steady current is flowing through a wire of uniform area of cross
section and having its resistance per unit length constant, potential
drop V across two points of the wire is directly proportional to the
length l between those two points.

Mathematically, Vαl

P ROCEDURE
1. Set up the electrical
circuit as shown in
Fig. A 6.1.
2. Connect positive
terminal of the battery
to point A (zero length)
of the potentiometer.
3. Connect negative end
of the battery to the
other end B (point) of
the potentiometer wire
through an ammeter,
plug key and a Fig. A 6.1 Circuit to study variation in potential drop
rheostat. The ammeter
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should be connected in such a way that its negative terminal is

connected to the negative terminal of the battery.
4. Connect positive end of the voltmeter to point A and other end to
a jockey J.
5. Now close the key K and press the jockey at point B. Adjust the
rheostat to get full scale deflection in voltmeter.
6. When jockey is pressed at point A, you will get zero deflection in
the voltmeter.
7. Now press the jockey at 40 cm and note the corresponding
voltmeter reading.
8. Repeat your observation by pressing the jockey at various lengths
like 80 cm, 120 cm etc. which may extend upto, say 400 cm of
potentiometer wire. Record voltmeter reading in each case as
shown in Table A 6.1.

O BSERVATIONS
Range of the voltmeter = ... V
Least count of the voltmeter = ...V
Zero error = ... V

Table A 6.1: Variation in potential drop with length

Sl. No. Length of potential wire over Voltmeter reading φ = V/l

which potential drop is V (V) (V cm–1)
measured l (cm)

1
2
--
5

Mean
C ALCULATIONS

The ratio ⎛⎜
V ⎞
⎝ l ⎟⎠ = φ is calculated. It is the potential gradient of the wire.
Its value is almost constant.

P LOTTING GRAPH
Plot a graph of V versus I, with V on y-axis and I on x-axis. Slope of
the line gives φ .
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R ESULT

V 
The ratio   = φ is found to be constant within the limits of
l
experimental error. Its mean value is... V cm–1.

The graph shows a linear relationship between V and l . The value of

V 
  = φ from the graph is ... V cm–1.
l

P RECAUTIONS
1. Zero error in the voltmeter and ammeter (if there is any) should
be corrected by adjusting the screw provided at the base of
the needle.
2. The current in the wire should remain constant throughout the
experiment. To ensure this, current should be drawn
intermittently for short duration of time. It should be monitored
by an ammeter and readjusted whenever necessary, with the help
of a rheostat.
3. Do not press the wire too hard with the jockey while noting down
the observations or else there is a possibility that the wire will
become non-uniform (diameter will change) at these points during
the course of time.
4. Check for uniformity of wire at its various points before the start
of the experiment. If wire is non-uniform, the potential gradient
will not be constant.

S
OURCES OF ERROR
1. The wire must have a uniform cross section along its entire
length. This should be checked by measuring its diameter at
various points before the start of the experiment.
2. Voltmeter may not give accurate reading.

D ISCUSSION
1. The potentiometer wire is connected firmly to thick copper
strips after every 100 cm of its length of 400 or 1000 cm.
However, these small sections of wire do not contribute to the
total length of the potentiometer wire since electrical current
flows through the copper strips rather than the potentiometer
wire in these sections.

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2. Potentiometer has the advantage that it draws no current from

the voltage source being measured. As such it is unaffected by
the internal resistance of the source.
3. If the graph is non-linear, what conclusion will you draw?

S ELF ASSESSMENT
1. A 100 cm wire of homogeneous material and uniform area of cross-
section form a square as shown in Fig. A 6.2. How can this
arrangement be used to select voltages 1/4, 1/2, 3/4 of the
voltage across AE.

2. A rheostat Rh used in laboratories along with a key K,

battery of emf E and internal resistance r is shown in
Fig. A 6.3. RL is some load resistance that represents
an auxiliary circuit which may be there in reality. If D
is the midpoint of the wire AB, what would be the
voltmeter reading? Does it depend on the value of RL or
Fig. A 6.2 RV, if RV represents the resistance of the voltmeter? Does
it depend on r ?

Fig. A 6.3

3. Consider a case in the above problem, wherein a potential

difference across ends A and B of the wire is 3 V. An experiment
requires a potential difference of 1.7 V as precise as possible.
Think of the possibilities of reducing emf of the source, using
another resistor in series or using a rheostat of the same resistance
but of greater length.
Is it possible to get negative potentials using the same circuit? If
yes, how?
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SUGGESTED ADDITIONAL EXPERIMENTS/ACTIVITIES

1. Connect a circuit as shown in Fig. A 6.3. Record potential difference at

various length l from end A. Plot a graph of V versus l. Obtain from the graph
the length that corresponds to 1.3 V. Draw a circuit diagram to show how
you can supply 1.3 V to an auxiliary circuit that works at 1.3 V.

2. A small circuit called the ‘level indicator’ (popularly known as dancing LED’s)
is available in the entertainment electronics market. It is often used in
stereophonic two-in-one recorders or graphic equalisers. Connect such a
circuit in place of a voltmeter in this activity and estimate the voltage levels
at which the LED’s in the array glow one after another.

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