To protect electrical devices (load) from jumps in power supply voltage, sometimes nonlinear semiconductor element varistor is used. They are connected in parallel with the load.

There are load $R_l=10~\Omega$, shunt $R=10~\Omega$ and varistor $v$ in the diagram. Current-voltage characteristic of the varistor is depicted below. In nominal mode ammeter's readings are $I=I_0=1.0~\mathrm{A}$.

1 Determine power supply voltage $\mathcal{E}_1$ in nominal mode. Also determine voltage $U_{v1}$ across the varistor and current $I_{v1}$ flowing through it.

2 Let power supply voltage increase two times ($\mathcal{E}_2 = 2 \mathcal{E}_1$). Determine new voltage $U_{v2}$ and current $I_{v2}$.