
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
474.6k+ views
3 likes
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,
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,
Here, is the capacitance of the first capacitor and is the maximum voltage that the first capacitor can withstand.
When we connect and in series, the maximum charge on the combination that it can withstand will be the charge on , since, numerically .
Therefore, the maximum charge on the combination of two capacitors will be,
Substituting and in the above equation, we get,
We have the formula for the equivalent capacitance of the series combination of capacitors,
Substituting and in the above equation, we get,
Now, the maximum voltage that the combination of capacitors can withstand is,
Substituting and in the above equation, we get,
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.
Formula used:
Charge,
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,
Here,
When we connect
Therefore, the maximum charge on the combination of two capacitors will be,
Substituting
We have the formula for the equivalent capacitance of the series combination of capacitors,
Substituting
Now, the maximum voltage that the combination of capacitors can withstand is,
Substituting
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.
Latest Vedantu courses for you
Grade 7 | CBSE | SCHOOL | English
Vedantu 7 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹45,300 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Why should a magnesium ribbon be cleaned before burning class 12 chemistry CBSE

A renewable exhaustible natural resources is A Coal class 12 biology CBSE

Megasporangium is equivalent to a Embryo sac b Fruit class 12 biology CBSE

What is Zeises salt and ferrocene Explain with str class 12 chemistry CBSE

How to calculate power in series and parallel circ class 12 physics CBSE

Anal style is present in A Male cockroach B Female class 12 biology CBSE
