In an ac circuit, the instantaneous current is zero,when the instantaneous voltage is maximum. In this case, the source may be connected to :
A. pure inductor.
B. pure capacitor.
C. pure resistor.
D. combination of an inductor and capacitor.
Choose the correct answer from the options given below :
A. pure inductor.
B. pure capacitor.
C. pure resistor.
D. combination of an inductor and capacitor.
Choose the correct answer from the options given below :
- A, B and C only
- B, C and D only
- A and B only
- A, B and D only
The Correct Option is D
Approach Solution - 1
Understanding the Phase Relationship in AC Circuits:
In an AC circuit: For a pure inductor, the current \( I \) lags the voltage \( V \) by \( 90^\circ \) (or \(\(\frac{\pi}{2}\) \) radians).
For a pure capacitor, the current \( I \) leads the voltage \( V \) by \( 90^\circ \). For a pure resistor, the current and voltage are in phase, meaning that they reach zero and maximum values simultaneously.
Condition for Instantaneous Current to be Zero When Voltage is Maximum:
The given condition (current is zero when voltage is maximum) implies a \( 90^\circ \) phase difference between the current and voltage.
This situation occurs in:
- A pure inductor, where current lags the voltage by \( 90^\circ \).
- A pure capacitor, where current leads the voltage by \( 90^\circ \).
- A combination of an inductor and capacitor (LC circuit), where the phase difference can also result in current being zero when voltage is maximum.
Conclusion:
Since this phase relationship is possible in a pure inductor, pure capacitor, or an LC combination, the correct answer is Option (4): A, B, and D only.
Approach Solution -2
In the given AC circuit, the instantaneous current is zero when the instantaneous voltage is maximum.
This means that the current and voltage are out of phase by 90° (a quarter of a cycle).
Step 2: Recall phase relations for different AC elements.
- For a pure resistor, current and voltage are in phase. Hence, when voltage is maximum, current is also maximum.
- For a pure inductor, current lags the voltage by 90°. Therefore, when the voltage is maximum, the current is zero.
- For a pure capacitor, current leads the voltage by 90°. Therefore, when the voltage is maximum, the current is again zero.
- For a combination of L and C, if the circuit is tuned such that the voltage and current are 90° out of phase (non-resonant case), the instantaneous current can still be zero when voltage is maximum.
Step 3: Analyze the condition.
Since the given condition (current = 0 when voltage = maximum) occurs when the current and voltage are 90° out of phase, this can happen in:
- A pure inductor
- A pure capacitor
- A non-resonant combination of inductor and capacitor
Step 4: Exclude the incorrect case.
A pure resistor cannot satisfy the given condition because current and voltage are in phase.
Step 5: Final Answer.
The correct cases are:
A, B, and D only
Final Answer:
\[ \boxed{A, B \text{ and } D \text{ only}} \]
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