# Electrical Resistance

Electrical resistance of a cylindrical wire of length $l$ and cross-sectional area $A$ is \begin{align} R=\rho\frac{l}{A} \end{align} where $\rho$ is the resistivity of the wire's material. The unit of resitance is ohms ($\Omega$).

The resistance of conductors usually increase with temperature as \begin{align} R_T=R_0\left(1+\alpha (T-T_0)\right) \end{align} where $R_0$ is resistance at temperature $T_0$, $R_T$ is the resistance at tempertaure $T$ and $\alpha$ is the thermal coefficient of resistance.

## Problems from IIT JEE

Problem (JEE Mains 2022): A 1 m long wire is broken into two unequal parts A and B. The A part of the wire is stretched into another wire C. Length of C is twice the length of A and the resistance of C is twice that of B. Find the ratio of length of A and B.

1. $1:4$
2. $1:2$
3. $4:1$
4. $2:1$

Problem (JEE Mains 2021) The resistance of a conductor at 15 deg C is 16 ohm and at 100 deg C is 20 ohm. What will be the temperature coefficient of resistance of the conductor?

1. 0.003 /deg C
2. 0.010 /deg C
3. 0.033 /deg C
4. 0.042 /deg C

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