Answer to Question #291477 in Electric Circuits for Ken

Question

A certain copper wire has a resistance of 25 ohms at 10 degrees Celsius. Take the temperature coefficient at 10 degrees Celsius to be 0.00405. What must be the maximum operating temperature of the wire if its resistance is to increase by at most 20%.

Answer 1

We know that

$R=R_0(1+\alpha∆T)$

$R=R_0(1+\alpha(T-T_0))$

$$R=R_0+25\times\frac{20}{100}=25+5=30\Omega$$

$30=25(1+0.00405(T-10)$

$\frac{30}{25}-1=0.00405(T-10)$

$0.2=0.00405(T-10)$

$49.38=T-10$

$T=59.30°C$