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In Figure 4, all of the capacitors have identical capacitance C, and the battery provides 60V. C1 60V C2 C4 C3 Figure 4 Consider the following scenarios, in each case starting with uncharged capacitors. Explain your answers.

Case I (a) While switch B is kept open, switch A is closed and then opened after C1, C2 and Cs are fully charged. What is the potential difference across each capacitor? (b) Subsequently switch B is closed. What is now the electric potential difference across each capacitor? Case II a) While switch A is kept open, switch B is closed. What is now the electric potential difference across each capacitor? (b) Subsequently switch A is closed. What is now the electric potential difference across each capacitor?

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Since. all capacitors are identical. So. when switch B is open. then. there would not be any charge stored in C4 because it is open circuit a) Consider Cl C2-C3-C4-c (let) Here, C1, C2 and C3 are in series, so, equivalent capacitance can be found as, eq eq Cea C eq So, charge stored in each capacitor in C1, C2, C3 CeV(60 V)-20 C voltSo, potential drop across C1- V,20 ot q 20 C volt Potentı al drop across C2 = ½ ,--=-. c-= 20 volt q20C volt = 20 volt Potential drop across C3 Potential drops across C4 0 yolt (due to open circuit) (b) Now, switch B is closed and A is open, in this case, C2 and C4 are in parallel, so, charge on C2 and C4 will redistribute in C2 and C4 equally because both - capacitors are identical So, charge on either C2 and C4 Since, voltage cross the capacitor is proportional to charge. So, if charge is half, then, voltage must be half of its initial value So, ½ = V, volt But voltage across C1 and C3 will be remaining same as it was initially So, VV3-20 volt 20 volt = 10 voltase 2 a) When switch A is opened, then, circuit will not be complete and charge will not be stored in any of the capacitor So, charge on each capacitor-(0 en, voltage drop across any of the capacitor-0 (b) When switch B is closed, then, C2 and C4 are in parallel, then, equivalent capacitance of C2 and C4, C24C+C-2 C Now, equivalent capacitance of all capacitors, 2C eq 5 So, charge on C 1 (C2&C4) and C3, q = Ce,V = (E) (60 volt) = 24C volt Voltage (d rop across C1 = 24 C volt 24 voltVoltage drop across C1V- Voltage drop across C324 volt Voltage drop across either C2 or C4 = V-V--= 24 e olt 24 volt . cm-24 volt = 24 2Colt-12 volt

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