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- Capacitance
NEET · Physics · Capacitance
Given below are two statements: one is labelled as Assertion (A)...
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): When two identical capacitors are connected in series across a battery, the total energy stored in the combination is twice the energy that would be stored in a single such capacitor connected across the same battery.
Reason (R): In a series combination, the equivalent capacitance decreases, and for a given voltage source, the total energy stored is directly proportional to the equivalent capacitance.
In the light of the above statements, choose the most appropriate answer from the options given below:
Assertion (A): When two identical capacitors are connected in series across a battery, the total energy stored in the combination is twice the energy that would be stored in a single such capacitor connected across the same battery.
Reason (R): In a series combination, the equivalent capacitance decreases, and for a given voltage source, the total energy stored is directly proportional to the equivalent capacitance.
In the light of the above statements, choose the most appropriate answer from the options given below:
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
D. (A) is false but (R) is true
Step-by-step solution
For a single capacitor of capacitance connected across a battery of voltage , the energy stored is .
When two such identical capacitors are connected in series, the equivalent capacitance becomes .
The total energy stored in the series combination across the same battery is . Thus, the total energy is halved, not doubled. Therefore, the Assertion (A) is false.
The energy stored for a given voltage source is . Since is constant, . In a series combination, decreases, which directly leads to a decrease in the total energy stored. Therefore, the Reason (R) is true.
Hence, (A) is false but (R) is true.
Answer: (A) is false but (R) is true
When two such identical capacitors are connected in series, the equivalent capacitance becomes .
The total energy stored in the series combination across the same battery is . Thus, the total energy is halved, not doubled. Therefore, the Assertion (A) is false.
The energy stored for a given voltage source is . Since is constant, . In a series combination, decreases, which directly leads to a decrease in the total energy stored. Therefore, the Reason (R) is true.
Hence, (A) is false but (R) is true.
Answer: (A) is false but (R) is true