The resistance of a conductor is 5,Omega at 5 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The resistance of a conductor at temperature $t$ is given by $R_t = R_0(1 + \alpha t)$,where $R_0$ is the resistance at $0\,^{\circ}C$ and $\alpha

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) The resistance of a conductor at temperature $t$ is given by $R_t = R_0(1 + \alpha t)$,where $R_0$ is the resistance at $0\,^{\circ}C$ and $\alpha$ is the temperature coefficient of resistance.Given:$R_1 = 5\,\Omega$ at $t_1 = 50\,^{\circ}C$$R_2 = 6\,\Omega$ at $t_2 = 100\,^{\circ}C$Using the ratio: $\frac{R_1}{R_2} = \frac{1 + \alpha t_1}{1 + \alpha t_2} \Rightarrow \frac{5}{6} = \frac{1 + 50\alpha}{1 + 100\alpha}$$5(1 + 100\alpha) = 6(1 + 50\alpha) \Rightarrow 5 + 500\alpha = 6 + 300\alpha$$200\alpha = 1 \Rightarrow \alpha = \frac{1}{200}\,^{\circ}C^{-1}$Now,substitute $\alpha$ into the equation for $R_1$: $5 = R_0(1 + \frac{1}{200} 	imes 50)$$5 = R_0(1 + 0.25) \Rightarrow 5 = R_0(1.25)$$R_0 = \frac{5}{1.25} = 4\,\Omega$.

The resistance of a conductor is $5\,\Omega$ at $50\,^{\circ}C$ and $6\,\Omega$ at $100\,^{\circ}C$. Its resistance at $0\,^{\circ}C$ is ................ $\Omega$.

Similar Questions

Masses of three wires of copper are in the ratio of $1: 3: 5$ and their lengths are in the ratio of $5: 3: 1$. The ratio of their electrical resistances is

$A$ nichrome wire $50 \text{ cm}$ long and $1 \text{ mm}^2$ cross-section carries a current of $4 \text{ A}$ when connected to a $2 \text{ V}$ battery. The resistivity of the nichrome wire in $\Omega \cdot \text{m}$ is:

The length of a given cylindrical wire is increased by $100 \%$. Due to the consequent decrease in diameter, the change in the resistance of the wire will be .................. $\%$

Masses of $3$ wires of same metal are in the ratio $1 : 2 : 3$ and their lengths are in the ratio $3 : 2 : 1$. The electrical resistances are in ratio

$A$ wire of resistance $4 \,\Omega$ is stretched to twice its original length. The resistance of the stretched wire would be ........... $\Omega$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module