Question

A thermistor may be assumed to have a linear temperature resistance over a limited temperature range. The variation in resistance is $0.05{/}^{\circ }C$ rise in temperature. The thermistor has a nominal resistance of $1000\Omega$ at ${20}^{\circ }C$. Supposing this thermistor is used in series with copper coil having resistance temperature coefficient of $0.004{/}^{\circ }C$ and nominal resistance $R_0$. If the resistance at ${20}^{\circ }C$ and ${25}^{\circ }C$ is the same for this series connected circuit comprising of coil and the thermistor, then the value of nominal resistance $\left(R_0\right)$ of copper coil (at $T={20}^{\circ }C)$ is _________ $k\Omega$.

• A. 15
• B. 10
• C. 7.5
• D. 12.5

Answer 1

The correct option is D 12.5

Since, the series equivalent resistance at ${20}^{\circ }C$ and ${25}^{\circ }C$ is given by

At ${20}^{\circ }C$

$R_{eq-{20}^{\circ }C}=1000+R_0$

At ${25}^{\circ }C$

$R_{eq-{25}^{\circ }C}=1000[1+(-0.05\left)5\right]+R_0[1+(0.004)\times 5]$

According to question

$R_{eq-{20}^{\circ }C}=R_{eq-{25}^{\circ }C}$

$1000+R_0=1000[1+(-0.05\left)5\right]+R_0[1+(0.004)\times 5]$

$R_0=12.5k\Omega$