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State ohm's law. In the circuit shown ...

State ohm's law.
In the circuit shown in figure, a voltmeter reads 30 volts when it is connected across 400 ohm resistance. Calculate what the same voltmeter will read when it is connected across the 300 ohm resistance.

A

30V

B

12.5V

C

15V

D

22.5V

Text Solution

Verified by Experts

The correct Answer is:
D
Change in the resistance of the conductor on increasing its temperature
`R-R_(0)=R_(0)alpha_(av)(T-T_(0))`
The disks will be effectively in series, so we will add the resistance to get the total. Looking only at pair of disk, we have
`R_(c)+R_(i)=R_(0_(C))(T-T_(0))+R_(0i)(alpha_(i)(T-T_(0))+1)`
`=R_(0_(C))+R_(0_(i))+(R_(0_(C))alpha_(c)+R_(0i)alpha_(i))(T-T_(0))`
This equation will only be constant if the coefficient for the term `(T-T_(0))` vanishes.
`"Then" R_(0_(c))+alpha_(c)+R_(0_(i)alpha_(i))=0`
but R=pL/A, and the disks have the same cross sectional area, so
`L_(c)rho_(c)alpha_(c)+L_(i)rho_(i)alpha_(i)=0`
`or (L_(c))/(L_(i))=-(rho_(i)alpha_(i))/(rho_(c)alpha_(c))=-(9.68xx10^(-8)xx6.5xx10^(-3))/(3500xx10^(-8)xx(-0.50xx10^(-3)))=0.036`
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