Determine the constant of variation for the stated condition.
-For a resistor in a direct current circuit that does not vary its resistance, the power that a resistor must dissipate is directly proportional to the square of the voltage across the resistor. The resistor must dissipate $\frac { 1 } { 16 }$ watt of power when the voltage across the resistor is 7 volts. Find the power that the resistor must dissipate when the voltage across it is 14 volts.
A) $\frac { 1 } { 4 }$ watt
B) $\frac { 1 } { 8 } \mathrm { watt }$
C) $\frac { 49 } { 16 }$ watts
D) $\frac { 7 } { 16 } \mathrm { watt }$

Question

Quizplus · Accepted Answer

The power $P$ dissipated by a resistor is directly proportional to the square of the voltage $V$ across it, so $P = kV^2$, where $k$ is the constant of proportionation. Given $P = \frac{1}{16}$ watt when $V = 7$ volts, we find $k = \frac{P}{V^2} = \frac{1/16}{49}$. When $V = 14$ volts, $P = k(14)^2 = \frac{1}{16} \times 4 = \frac{1}{4}$ watt.

Determine the Constant of Variation for the Stated Condition 116\frac { 1 } { 16 }161​

Determine the Constant of Variation for the Stated Condition $\frac { 1 } { 16 }$