An alternating voltge is represented by $$\mathrm{V}=80 \sin (100 \pi \mathrm{t}) \cos (100 \pi \mathrm{t})$$ volt. The peak voltage is

A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$$\omega$$'. Keeping the voltage same, if the frequency is changed to $$\frac{\omega}{3}$$ the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

An inductive coil has a resistance of $$100 ~\Omega$$. When an a.c. signal of frequency $$1000 \mathrm{~Hz}$$ is applied to the coil the voltage leads the current by $$45^{\circ}$$. The inductance of the coil is $$\left(\tan 45^{\circ}=1\right.$$)

In an ideal step down transformer, out of the following quantities, which quantity increases in the secondary coil?