Electron of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' is travelling with speed '$$v$$' along a circular path of radius '$$R$$', at right angles to a uniform magnetic field of intensity '$$B$$'. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

In a series LR circuit, $$X_L=R$$, power factor is $$P_1$$. If a capacitor of capacitance $$C$$ with $$X_C=X_L$$ is added to the circuit the power factor becomes $$P_2$$. The ratio of $$P_1$$ to $$P_2$$ will be

If only $$1 \%$$ of total current is passed through a galvanometer of resistance '$$G$$' then the resistance of the shunt is

A voltmeter of resistance $$150 \Omega$$ connected across a cell of e.m.f. $$3 \mathrm{~V}$$ reads $$2.5 \mathrm{~V}$$. What is the internal resistance of the cell?