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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.

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bawbdmo

THe problem is basically telling us: [tex] P=kV^2 [/tex]

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

[tex] \frac{1}{16}=k*14^2\implies\\
\frac{1}{16*196}=k \implies \\
\frac{1}{3136}=k [/tex]

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

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