Two conductors have the same resistance at 0, | vedclass

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

Question

(D) Let $R_0$ be the initial resistance of both conductors at $0\,^{\circ}C$.At temperature $	heta$,their resistances are given by:$R_1 = R_0(1 + \al

Vedclass · Accepted Answer

$\frac{\alpha_1 + \alpha_2}{2}$

Vedclass · Answer

(D) Let $R_0$ be the initial resistance of both conductors at $0\,^{\circ}C$.At temperature $	heta$,their resistances are given by:$R_1 = R_0(1 + \alpha_1 	heta)$$R_2 = R_0(1 + \alpha_2 	heta)$For a series combination,the total resistance $R_s$ is the sum of individual resistances:$R_s = R_1 + R_2$Let $\alpha_s$ be the temperature coefficient of the series combination. Then:$R_{s0}(1 + \alpha_s 	heta) = R_1 + R_2$Since $R_{s0} = R_0 + R_0 = 2R_0$,we have:$2R_0(1 + \alpha_s 	heta) = R_0(1 + \alpha_1 	heta) + R_0(1 + \alpha_2 	heta)$$2R_0 + 2R_0 \alpha_s 	heta = 2R_0 + R_0 	heta(\alpha_1 + \alpha_2)$Dividing both sides by $2R_0 	heta$:$\alpha_s = \frac{\alpha_1 + \alpha_2}{2}$

Two conductors have the same resistance at $0\,^{\circ}C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficient of their series combination is

Similar Questions

Three resistances of magnitude $2\,\Omega$,$3\,\Omega$,and $5\,\Omega$ are connected in parallel to a battery of $10\,V$ and of negligible resistance. The potential difference across the $3\,\Omega$ resistance will be ............... $V$.

Four resistances of $100 \ \Omega$ each are connected in the form of a square. Then,the effective resistance along the diagonal points is ............. $\Omega$.

Some electric bulbs are connected in series across a $220\, V$ supply in a room. If one bulb is fused,then the remaining bulbs are connected again in series across the same supply. The illumination in the room will

An electric kettle has two filaments. The first filament boils a certain amount of water in $10 \text{ minutes}$ and the second filament boils it in $15 \text{ minutes}$. If both filaments are connected in parallel,the water will boil in .............. minutes.

Find the equivalent resistance between $P$ and $Q$. (If each wire has a resistance $R$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module