Two resistances equal at 0C with temperature coefficient of resistance - 1 and - 2 joined in series act as a single resistance in a circuit- The temperature coefficient of their single resistance will be

The correct option is C α _1+α _2/2 R_1=R_0 ( 1+α _1t )+R_0 ( 1+α _2t ) =2R_0 ( 1+α _1+α _2/2 t ) Comparing with R=R_0 ( 1+α t ) α= ...

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Standard XII

Physics

Thermal Expansion

Two resistanc...

Question

Two resistances equal at $0^{C}$ with temperature coefficient of resistance $α_{1}$ and $α_{2}$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

α_{1} + α_{2}

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\frac{α_{1} α_{2}}{α_{1} + α_{2}}

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\frac{α_{1} - α_{2}}{2}

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\frac{α_{1} + α_{2}}{2}

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Solution

The correct option is C $\frac{α_{1} + α_{2}}{2}$
$R_{1} = R_{0} (1 + α_{1} t) + R_{0} (1 + α_{2} t)$
$= 2 R_{0} (1 + \frac{α_{1} + α_{2}}{2} t)$
Comparing with $R = R_{0} (1 + α t)$
$α = \frac{α_{1} + α_{2}}{2}$

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Two resistances equal at 0C with temperature coefficient of resistance α1 and α2 joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

The correct option is C α1+α22R1=R0(1+α1t)+R0(1+α2t)=2R0(1+α1+α22t)Comparing with R=R0(1+αt)α=α1+α22

Two resistances equal at $0^{C}$ with temperature coefficient of resistance $α_{1}$ and $α_{2}$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be

The correct option is C $\frac{α_{1} + α_{2}}{2}$
$R_{1} = R_{0} (1 + α_{1} t) + R_{0} (1 + α_{2} t)$
$= 2 R_{0} (1 + \frac{α_{1} + α_{2}}{2} t)$
Comparing with $R = R_{0} (1 + α t)$
$α = \frac{α_{1} + α_{2}}{2}$