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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): Five identical capacitors, each of capacitance , are connected to form a balanced Wheatstone bridge. If the central capacitor is replaced by a thick conducting wire, the equivalent capacitance of the network becomes .
Reason (R): In a balanced Wheatstone bridge, the two nodes connecting the central branch are at the same potential.
In the light of the above statements, choose the most appropriate answer from the options given below:
Assertion (A): Five identical capacitors, each of capacitance , are connected to form a balanced Wheatstone bridge. If the central capacitor is replaced by a thick conducting wire, the equivalent capacitance of the network becomes .
Reason (R): In a balanced Wheatstone bridge, the two nodes connecting the central branch are at the same potential.
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
Reason (R) is true: The defining condition of a balanced Wheatstone bridge is that the ratio of capacitances in the adjacent arms is equal, which results in the two nodes of the central branch being at the same potential.
Assertion (A) is false: Because the two central nodes are at the same potential, replacing the central capacitor with a conducting wire (short circuit) will not cause any charge to flow between these nodes. The charge distribution remains completely undisturbed.
Alternatively, if the central branch is shorted, the circuit can be viewed as two parallel combinations in series. The first half has two capacitors in parallel (), and the second half has two capacitors in parallel (). The equivalent capacitance is the series combination of these two halves: . Thus, the equivalent capacitance remains , not .
Answer: (A) is false but (R) is true
Assertion (A) is false: Because the two central nodes are at the same potential, replacing the central capacitor with a conducting wire (short circuit) will not cause any charge to flow between these nodes. The charge distribution remains completely undisturbed.
Alternatively, if the central branch is shorted, the circuit can be viewed as two parallel combinations in series. The first half has two capacitors in parallel (), and the second half has two capacitors in parallel (). The equivalent capacitance is the series combination of these two halves: . Thus, the equivalent capacitance remains , not .
Answer: (A) is false but (R) is true