The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance of the circuit becomes a pure conductance at all frequencies is ________.

In the portion of a circuit shown, if the heat generated in 5 Ω resistance is 10 calories per second then heat generated by the 4 Ω resistance, the calories per second, is ______.

A dc voltage with ripple is given by $$v\left( t \right)\,\,\,\, = \,\,\,\,\left[ {100 + 10\sin \left( {\omega t} \right) - 5\sin \left( {3\omega t} \right)} \right]$$ volts. Measurements of this voltage $$v\left( t \right),$$ made by moving-coil and moving iron voltmeters, show readings of $${V_1}$$ and $${V_2}$$ respectively. The value of $${V_2} - {V_1},$$ in volts, is _______.

A three-phase, $$50$$ $$Hz$$ salient-pole synchronous motor has a per-phase direct-axis reactance $$\left( {{X_d}} \right)$$ of $$0.8$$ $$pu$$ and a per-phase quadrature-axis reactance $$\left( {{X_q}} \right)$$ of $$0.6$$ $$pu.$$ Resistance of the machine is negligible. It is drawing full-load current at $$0.8$$ $$pf$$ (leading). When the terminal voltage is $$1$$ $$pu,$$ per-phase induced voltage, in $$pu,$$ is ______________.