Page 185 - NCERT Science Class 10 English Medium

Example 11.4
The potential difference between the terminals of an electric heater
is 60 V when it draws a current of 4 A from the source. What current
will the heater draw if the potential difference is increased to 120 V?
Solution
We are given, potential difference V = 60 V, current I = 4 A.

V 60 V
According to Ohm’s law, R = = = 15 Ω .
I 4 A
When the potential difference is increased to 120 V the current is
given by
V 120 V
current = = = 8 A .
R 15 Ω
The current through the heater becomes 8 A.

Example 11.5
Resistance of a metal wire of length 1 m is 26 Ω at 20°C. If the
diameter of the wire is 0.3 mm, what will be the resistivity of the
metal at that temperature? Using Table 11.2, predict the material
of the wire.
Solution
We are given the resistance R of the wire = 26 Ω, the diameter
-4
d = 0.3 mm = 3 × 10 m, and the length l of the wire = 1 m.
Therefore, from Eq. (11.10), the resistivity of the given metallic wire is
2
ρ = (RA/l) = (Rπd /4l )
Substitution of values in this gives
–6
ρ = 1.84 × 10 Ω m
The resistivity of the metal at 20°C is 1.84 × 10 –6 Ω m. From
Table 11.2, we see that this is the resistivity of manganese.

Example 11.6
A wire of given material having length l and area of cross-section A
has a resistance of 4 Ω. What would be the resistance of another wire
of the same material having length l/2 and area of cross-section 2A?
Solution
For first wire

l
R = ρ = 4Ω
1 A
Now for second wire
l /2 1 l
R = ρ = ρ
2
2A 4 A
1
R = R
2 1
4
R = 1Ω
2
The resistance of the new wire is 1Ω.

180 Science

2024-25