Two wires with temperature coefficients of re | vedclass

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

Question

(C) For two resistors in series,the total resistance at temperature $t$ is given by $R_t = R_{1t} + R_{2t}$.Given $R_{1t} = R_1(1 + \alpha_1 t)$ and $

Vedclass · Accepted Answer

$\frac{R_1 \alpha_1 + R_2 \alpha_2}{R_1 + R_2}$

Vedclass · Answer

(C) For two resistors in series,the total resistance at temperature $t$ is given by $R_t = R_{1t} + R_{2t}$.Given $R_{1t} = R_1(1 + \alpha_1 t)$ and $R_{2t} = R_2(1 + \alpha_2 t)$.Substituting these into the total resistance equation:$R_t = R_1(1 + \alpha_1 t) + R_2(1 + \alpha_2 t)$$R_t = (R_1 + R_2) + (R_1 \alpha_1 + R_2 \alpha_2)t$$R_t = (R_1 + R_2) \left[ 1 + \frac{R_1 \alpha_1 + R_2 \alpha_2}{R_1 + R_2} t \right]$Comparing this with the standard form $R_t = R_{total}(1 + \alpha_{eff} t)$,where $R_{total} = R_1 + R_2$,we get:$\alpha_{eff} = \frac{R_1 \alpha_1 + R_2 \alpha_2}{R_1 + R_2}$.

Two wires with temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ have resistances $R_1$ and $R_2$ at $0^{\circ}C$. If they are connected in series,what is the effective temperature coefficient of resistance?

Similar Questions

You are given $10$ resistors each of resistance $2 \ \Omega$. First,they are connected to obtain the possible minimum resistance. Then,they are connected to obtain the possible maximum resistance. The ratio of maximum and minimum resistance is . . . . . . .

In the circuit diagram shown,each resistor has a resistance of $1\,\Omega$. Find the equivalent resistance between $A$ and $B$.

$A$ uniform ring of conducting wire of radius $r$ has resistance $R$. $A$ and $B$ are two points on the ring which subtend an angle $\theta$ at the centre of the ring. The equivalent resistance between points $A$ and $B$ is:

Six wires, each of resistance $r$, are connected so as to form a tetrahedron. The equivalent resistance of the combination when current enters through one corner and leaves through some other corner is

Eight resistances each of resistance $5\,\Omega$ are connected in the circuit as shown in the figure. The equivalent resistance between $A$ and $B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module