Q.
In the circuit shown in the figure, if switches S1 and S2 have been closed for a long time, then charge on the capacitor
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a
1s 100 μC
b
increases to 200 μC if one third of the gap of the capacitor's plates is filled with a dielectric (K = 2) of same area
c
remains unchanged if one third of the gap of the capacitor's plates is filled with,a dielectric (K = 2) of same area.
d
both (1) and (2)
answer is D.
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Detailed Solution
After long time, current through the capacitor = 0 Current through 6 Ω resistor, i=12−48 =1AVoltage across capacitor, V = 4 + (6) (1) = 10 VCharge on the capacitor, Q=10 10 = 100 μCAfter the insertion of dielectricC'=Aε0d3+d3+d32 = Aε0d 113 +13 +16 =10 15/6 = 65 10=12 μFHere voltage across capacitor remains same.∴ Charge on the capacitor, Q'=12 10 = 120 μC
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