Question

For a resistor in a direct current circuit that does not vary its resistance, the power that a resistor must dissipate is directly proportional ti the square of the voltage across the resistor. The resistor must dissipate 1/16 watt of power when the voltage across the resistor is 14 volts. Find the power that the resistor must dissipate when the voltage across it is 42 volts.

Answer 1

THe problem is basically telling us: $P=kV^2$

where P is the power disappated and V^2 is our voltage squared.

$\frac{1}{16}=k*14^2\implies\\ \frac{1}{16*196}=k \implies \\ \frac{1}{3136}=k$

So, for the second example to find the power we simply have to plug k and our voltage back in, so:$P=\frac{14^2*3^2}{14^2*6} \implies \\ P=\frac{9}{6}= \frac{3}{2}$