A parallel plate condenser is filled with two dielectrics as shown in figure. Area of each pate is Am2 and the separation is d metre. The dielectric constants are K1 and K2 respectively. Its capacitance (in farad) will be :
2∈0Ad(K1+K2K1K2)
2∈0Ad(K1K2K1+K2)
∈0AK1K22(d2K1+d1K2)
∈0Ad(K1+K22K1K2)
A
2∈0Ad(K1+K2K1K2)
B
2∈0Ad(K1K2K1+K2)
C
∈0Ad(K1+K22K1K2)
D
∈0AK1K22(d2K1+d1K2)
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Solution
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Capacitance of first half of the capacitor of width d/2=C1=K1Aϵ0d/2=2K1Aϵ0d
Similarly the capacitance of other half =C2=2K2Aϵ0d
These two capacitance are connected in series.
Thus, the net capacitance of the combination is, Ceff=C1C2C1+C2=2Aϵ0d(K1K2K1+K2)
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