Two capacitors arc charged by different voltage sources The

Two capacitors arc charged by different voltage sources. The first is a pair of nested 0f average radius R_1 = 7 em separation di = 12.5 pm. is filled with a dielectric with k. - 1.6. and the inner surface is charged so that V_1 - 100 V. The sccond is made from parallel plates with a capacitance G - 50 nF and holds a charge qi = 5.2 muC Make a table of the capacitance, charge voltage and potential energy on each of the two capacitors.; Without doing any calculation, if the two arc hooked together in parallel (i.e. (+) to (+) and (-) to (-)). which one will gain chargc and which one will lose charge? Explain your reasoning What is the equivalent capacitance C_af of the two in parallel? What is the final voltage of the two in parallel ? much energy was lost in the process of connecting the two in parallel? Going back to the original condition, what will be the final voltage V/s if the two are connected in a series loop (i.e. (+) to (-) and (-) to (+))? (this configuration has the same equivalent capacitance Cy as in part (c) above!) How much energy A Us will be lost in the process of connecting the two together in series?

Solution

a)

capacitacne of nested shells

C=Ke_oA/d

C₁=1.6*(8.85*10^-12)*(pi*0.7)²/(12.5*10^-6)

C₁=17.44 nF

Charge on C1 is

Q₁=C₁V₁ =(17.44*10^-9)*100 =1.744 uC

Energy stored in C1 is

U₁=(1/2)C₁V₁² =(1/2)(1.744*10^-8)*100² =0.0872 mJ

For Capcitor C2 ,the voltage is

V₂=Q₂/C₂ = 5.2*10^-6/(50*10^-9) =104 Volts

Energy stored in C2 is

U₂=(1/2)C₂V₂²=(1/2)(50*10^-9)*104² =0.2704 mJ

b)

Since charge moves from higher to lower potential ,so it moves from C₂ to C₁ untill the potential difference across the capacitors are equal.So C₁ gain charge and C₂ loses charge .

c)

equivalent capacitance

C_eq =50+17.44 =67.44 nF

d)

Final voltage across the both both the capacitors is same

V_final=(C₁V₁+C₂V₂)/(C₁+C₂) =17.44*100+50*104/(17.44+50)

V_final=102.97 Volts =103 Volts(approx)

S.no	Capacitance(nF)	Voltage(V)	Charge(uC)	Potential Energy(mJ)
1	17.44	100	1.744	0.0872
2	50	104	5.2	0.2704