Question #42718

A non-linear electronic device $D$ has a voltage-current characteristic given by $I = k V^3$, where $k = 1.0 \times 10^{-3} \text{ A/V}^3$. The device is connected in series with a linear resistor $R$ and a DC voltage source of EMF $E = 10.0 \text{ V}$ (with negligible internal resistance). Under DC steady-state conditions, the voltage drop across the non-linear device is measured to be $V_D = 2.0 \text{ V}$. A small AC voltage signal $v(t) = v_0 \sin(\omega t)$ with amplitude $v_0 = 16.25 \text{ mV}$ is then added in series with the DC source. Assuming the AC signal is small enough that the dynamic resistance of the device remains constant, what is the amplitude of the resulting AC current in the circuit?