The reading of the ammeter () in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is _____ .
- A
- B
- C
- D
The reading of the ammeter () in steady state in the following circuit (assuming negligible internal resistance of the ammeter) is _____ .
Correct answer:C
Standard Method
Given: The ammeter reading in the circuit is required in steady state.
Find: The current through the ammeter.
In DC steady state, a capacitor behaves as an open circuit and does not allow current to pass through its branch.
Therefore, the diagonal branch containing the capacitor is effectively removed from conduction, and the remaining circuit is symmetrically arranged.
Because the resistances on both sides of the ammeter are identical, equal currents tend to flow through the ammeter in opposite directions.
Hence these equal and opposite currents cancel each other, so the net current through the ammeter is .
Therefore, the reading of the ammeter is . The correct option is C.
Symmetry Trick
Given: The circuit is in steady state and contains a capacitor.
Find: The ammeter reading.
Use two quick observations:
By symmetry, the potentials at the two ends of the ammeter become equal, so there is no potential difference across it.
Since
if across the ammeter, the current through it is also .
Therefore, the ammeter reads , so the correct option is C.
Assuming the capacitor still conducts current in steady state. This is wrong because an ideal capacitor blocks DC after a long time. Treat the capacitor branch as an open circuit before analyzing the rest of the network.
Ignoring circuit symmetry after removing the capacitor branch. This is wrong because the ammeter lies between symmetric parts of the circuit, leading to equal and opposite current contributions. Check symmetry before applying lengthy calculations.
Thinking that the ammeter must show a non-zero current because it is physically connected in the circuit. This is wrong because current through an ammeter depends on the potential difference across it, which can be zero in a balanced symmetric network.
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