To find the current through the conductor at
220∘C, we need to understand the relationship between temperature and resistance, assuming that the resistance of the conductor increases linearly with temperature. This relationship is given by:
RT=R0(1+αT)Where:
RT is the resistance at temperature
T.
R0 is the resistance at
0∘C.
α is the temperature coefficient of resistance.
T is the temperature in degrees Celsius.
Since the current
I is inversely proportional to the resistance
R (Ohm's Law:
I=‌ ), we'll first express the given currents
a and
b at the corresponding temperatures in terms of resistance:
At
0∘C :
I0=a=‌At
100∘C :
I100=b=‌=‌ Dividing the equations for
b by the equation for
a, we get:
‌=‌=‌=‌Solving for
α, we get:
‌1+100α=‌‌100α=‌−1‌α=‌(‌−1) Now let's determine the current at
220∘C :
At
220∘C :
I220=‌=‌ Substituting the value of
α from above:
‌I220=‌| V |
| R0(1+220⋅‌(‌−1)) |
‌I220=‌‌I220=‌‌I220=‌‌I220=‌‌I220=‌ Using
I0=‌ from above:
‌I220=‌‌I220=‌ Multiplying numerator and denominator by 5 , we get:
I220=‌Therefore, the current through the conductor at
220∘C is given by Option C :
‌