Physics · Alternating currents, peak and RMS value of alternating current/voltage
In a black box of unknown elements or or any other combination), an ac voltage \
In a black box of unknown elements \( (\boldsymbol{L} \) or \( R \) or any other combination), an ac voltage \( \boldsymbol{E}=\boldsymbol{E}_{0} \sin (\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}) \) is applied and current in the circuit was found to be \( \boldsymbol{I}=\boldsymbol{I}_{0} \sin [\boldsymbol{\omega} \boldsymbol{t}+\boldsymbol{\phi}+(\boldsymbol{\pi} / \mathbf{4})] . \) Then the unknown elements in the box may be
- A. Only capacitor
- B. Inductor and resistor both
- C. Either capacitor, resistor, inductor or only capacito and resistor
- D. only resistor
Step-by-step solution
The current leads the voltage by 45°, indicating a capacitive circuit with resistance. A pure capacitor gives 90° lead, pure resistor gives 0°, and inductor-resistor gives lag. Only a combination including a capacitor and resistor (or a more general capacitive circuit) can produce a 45° lead. Option C includes this possibility, while other options are incorrect.
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