In the figure, transformer $${T_1}$$ has two secondaries, all three windings having the same number of turns and with polarities having the same number of turns and with polarities as indicated. One secondary is shorted by a $$10\,\Omega $$ resistor $$R,$$ and the other by a $$15\mu F$$ capacitor. The switch $$SW$$ is opened $$(t=0)$$ when the capacitor is charged to $$5$$ $$V$$ with the left plate as positive. At $$t=0+$$ the voltage $${V_P}$$ and current $${I_R}$$ are

A $$3$$ $$V$$ $$dc$$ supply with an internal resistance of $$2\,\,\Omega $$ supplies a passive non-linear resistance characterized by the relation $${V_{NL}} = {\rm I}_{NL}^2.$$ The power dissipated in the non-linear resistance is

The probes of a non $$-$$ isolated, two-channel oscilloscope are clipped to points $$A, B, $$ and $$C$$ in the circuit of the adjacent fig. $${V_{in}}$$ is a square wave of a suitable low frequency. The display on $$c{h_1}$$ and $$c{h_2}$$ are as shown on the right. Then the ''signal'' and ''Ground'' probes $${S_1},\,\,{G_1}$$ and $${S_2},\,\,{G_2}$$ of $$c{h_1}$$ and $$c{h_2}$$ respectively are connected to points.

A three phase squirrel cage induction motor has a starting current of seven times the full load current and full load slip of $$5\% $$

If a starting torque of $$0.5$$ per unit is required then the per unit starting current should be