Electrostatics

Problem 135: Three condensers of 6, 10 and 15 \(\mu F\) are connected in series across a 200 V supply. If the condensers are disconnected, how much energy can the charged condensers provide if connected across each other with like polarities together?

Problem 136: Two capacitors with capacitance of 6 \(\mu F\) and 4 \(\mu F\) are connected in series across a 100 V dc source. If the supply voltage is cut-off and the two capacitors are connected in parallel, what will be the final charge accumulated in the 4 \(\mu F\) capacitor?

Problem 137: A 40 \(\mu F\) capacitor is charged to store 0.2 J of energy. An uncharged 60 \(\mu F\) capacitor is connected in parallel with the first one through a perfectly conducting leads. What is the energy lost due to the work done by the charges in spreading out over the two capacitors?

Problem 138: Four capacitors A, B, C and D are connected across a 150-V DC source. The charges accumulated in A, B and C are equal to 2000, 750 and 1500 \(\mu C\), respectively. If the total capacitance of the combination is known to be 35 \(\mu F\), how much charge is the accumulated in capacitor D?

Problem 139: A condenser of 1 microfarad capacitance is charged to 100 volts and then disconnected from the power supply. A second but uncharged capacitor of 3 microfarad is then connected across the first capacitor. The voltage across the parallel combination is

Problem 140: Three capacitors A, B and C are charged as follows: A = 10 \(\mu F\), 100 V; B = 15 \(\mu F\), 150 V and C = 25 \(\mu F\), 200 V. They are connected in parallel with terminals of like polarity together. What is the voltage across the combination?

Problem 141: A 100 \(\mu F\) capacitor is charged from a 200-V supply. The charged capacitor is then connected across three uncharged capacitors connected in parallel. The charges on these capacitors after a long time become 4000, 5000 and 6000 \(\mu C\). Solve the voltage across the combination.

Problem 142: Two capacitors of 200 and 800 nF, respectively are connected in parallel. The combination is then connected in series with another two capacitors of C and 600 nF connected in parallel. If the total capacitance of the set-up is 500 nF, determine the capacitance C.

Problem 143: A coaxial cable has a 10-mm diameter inside conductor and a metallic sheath with an inside diameter of 20 mm. If the insulating medium has a dielectric constant, k = 2, and a permittivity of \(1.113\times10^{-10}\), what is the capacitance between the conductor and the shield per km?

Problem 144: A lead-sheath cable for underground service has a copper conductor (diameter =0.350 inch) surrounded by 0.20-inch wall of rubber insulation. Assuming the dielectric constant of 4.3 for rubber, calculate the capacitance of the cable per mile length.