Electric Potential Difference

A metal rod of square cross-sectional area A having length l has current I flowing through it when a potential difference of V volt is applied across its ends (figure I). Now the rod is cut parallel to its length into two identical pieces and joined as shown in figure II. What potential difference must be maintained across the length of 2l. so that the current in the rod is still I?

An α-particle and a proton are accelerate at same potential difference from rest. What will be the ratio of their final velocity?

Draw a labelled diagram of Van de Graaff generator. State its working principle to show how by introducing a small charged sphere into a larger sphere, a large amount of charge can be transferred to the outer sphere. State the use of this machine and also point out its limitations.

A charge of 20 µC is placed on the positive plate of an isolated parallel-plate capacitor of capacitance 10 µF. Calculate the potential difference developed between the plates.

The potential difference applied across a given resistor is altered so that the heat produced per second increases by a factor of 9. By what factor does the applied potential difference change?

The capacitance between the adjacent plates shown in figure is 50 nF. A charge of 1⋅0 µC is placed on the middle plate. (a) What will be the charge on the outer surface of the upper plate? (b) Find the potential difference developed between the upper and the middle plates.

Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of mass 1.96 × 10^–15 kg is suspended in equilibrium between the plates. If e is the elementary charge, then charge on the particle is ______.

Explain the principle of a device that can build up high voltages of the order of a few million volts.