## College Physics (4th Edition)

It takes more energy to increase the current from $10~mA$ to $20~mA$ than to increase the current from $0~mA$ to $10~mA$.
We can write an expression for the energy stored in an inductor: $U = \frac{1}{2}~L~I^2$ Let $U_1 = \frac{1}{2}~L~I_1^2$ be the energy required to increase the current from $0~mA$ to $10~mA$. We can find the energy stored in the inductor when the current is $20~mA$: $U_2 = \frac{1}{2}~L~I_2^2$ $U_2 = \frac{1}{2}~L~(2~I_1)^2$ $U_2 = 4\times \frac{1}{2}~L~I_1^2$ $U_2 = 4\times U_1$ We would need to provide energy in the amount of $4U_1-U_1 = 3U_1$ to increase the current from $10~mA$ to $20~mA$. Therefore, it takes more energy to increase the current from $10~mA$ to $20~mA$ than to increase the current from $0~mA$ to $10~mA$.