# 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.

- $1:4$
- $1:2$
- $4:1$
- $2:1$

**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?

- 0.003 /deg C
- 0.010 /deg C
- 0.033 /deg C
- 0.042 /deg C

## Related

- Colour code for resistors
- Series and Parallel Arrangements of Resistances
- Wheatstone bridge
- Symmetry in electrical circuits
- Resistance of an Electric Bulb
- Specific resistance of the material of a wire using meter bridge and post office box
- Ohm's Law
- Resistance (Expt)