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A capacitor of 1 mF withstands a maximum voltage 6KV while another capacitor 2 mF withstands a maximum voltage of 4KV. If the capacitors are connected in series, the system will withstand a maximum voltage of
A. 2 KV
B. 4 KV
C. 6 KV
D. 9 KV

Answer
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Hint:On connecting the two capacitors in series, the charge on each capacitor becomes equal. The maximum charge on the capacitor combination is equal to charge on the first capacitor. Determine the equivalent capacitance of the series combination of two capacitors. Use the formula for the potential difference across the capacitor.

Formula used:
Charge, Q=CV
where, C is the capacitance and V is the voltage.

Complete step by step answer:
We know that the charge remains conserved in the series combination. Therefore, when we connect two capacitors of different capacitors in series, the charge on both the capacitors becomes equal.
We have, the maximum charge on the first capacitor is,
Q1=C1V1
Here, C1 is the capacitance of the first capacitor and V1 is the maximum voltage that the first capacitor can withstand.

When we connect C1 and C2 in series, the maximum charge on the combination that it can withstand will be the charge on C1, since, numerically C1V1<C2V2.
Therefore, the maximum charge on the combination of two capacitors will be,
Qmax=C1V1
Substituting C1=1mF and V1=6KV in the above equation, we get,
Qmax=(1×103F)(6×103V)
Qmax=6C

We have the formula for the equivalent capacitance of the series combination of capacitors,
1Ceq=1C1+1C2
Ceq=C1C2C1+C2
Substituting C1=1mF and C2=2mF in the above equation, we get,
Ceq=(1)(2)1+2
Ceq=23mF

Now, the maximum voltage that the combination of capacitors can withstand is,
Vmax=qmaxCeq
Substituting Qmax=6C and Ceq=23mF in the above equation, we get,
Vmax=623
Vmax=182
Vmax=9V
Therefore, the maximum voltage that the two series capacitors can withstand is 9 V.

So, the correct answer is option D.

Note:When the capacitors are connected in series, the charge on each capacitor becomes equal regardless of the capacitance since the current has to pass through each capacitor. In this case, the charge on each capacitor will be equal to the charge on the first capacitor in the path of current. Do not get confused between the formulae for equivalent capacitance and equivalent resistance since the formulae are quite similar but are actually opposite for series combination and parallel combination.
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