A coil of inductance 1 H and resistance $$100 \,\Omega$$ is connected to a battery of 6 V. Determine approximately :

(a) The time elapsed before the current acquires half of its steady - state value.

(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given $$\ln 2=0.693, \mathrm{e}^{-3 / 2}=0.25$$)

A transformer operating at primary voltage $$8 \,\mathrm{kV}$$ and secondary voltage $$160 \mathrm{~V}$$ serves a load of $$80 \mathrm{~kW}$$. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

The equation of current in a purely inductive circuit is $$5 \sin \left(49\, \pi t-30^{\circ}\right)$$. If the inductance is $$30 \,\mathrm{mH}$$ then the equation for the voltage across the inductor, will be :

$$\left\{\right.$$ Let $$\left.\pi=\frac{22}{7}\right\}$$

A series LCR circuit has $$\mathrm{L}=0.01\, \mathrm{H}, \mathrm{R}=10\, \Omega$$ and $$\mathrm{C}=1 \mu \mathrm{F}$$ and it is connected to ac voltage of amplitude $$\left(\mathrm{V}_{\mathrm{m}}\right) 50 \mathrm{~V}$$. At frequency $$60 \%$$ lower than resonant frequency, the amplitude of current will be approximately :