Physics-12 : 7: Alternating Current - Flashcards

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What is the average power dissipated in a resistor over a cycle?
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\( \bar{p} = \frac{1}{2} i_m^2 R \).
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# Question Answer
1 What is the average power dissipated in a resistor over a cycle? \( \bar{p} = \frac{1}{2} i_m^2 R \).
2 Does Ohm's law hold for AC circuits with pure resistors? Yes.
3 What is the phase relationship between voltage and current in a pure inductor? Current lags voltage by \( \frac{\pi}{2} \).
4 Are voltage and current phasors in the same direction for a pure resistor? Yes.
5 What is the average power dissipated in a pure capacitor over a complete cycle? Zero.
6 What is the SI unit of capacitive reactance? Ohm (\( \Omega \)).
7 When does the current lag the voltage in a series LCR circuit? When \( X_L > X_C \) (inductive circuit).
8 What is the relationship between the voltage phasors in a series LCR circuit? \( \mathbf{V} = \mathbf{V}_R + \mathbf{V}_L + \mathbf{V}_C \).
9 What is the power factor? \( \cos\phi \).
10 Can resonance occur in an RL or RC circuit? No.
11 What is a step-down transformer? A transformer in which the secondary voltage is less than the primary voltage (\( N_s < N_p \)).
12 What is the power factor in Example 7.8? 0.6.
13 What are the main sources of energy loss in a transformer? Flux leakage, resistance of windings, eddy currents, and hysteresis.
14 A 60 µF capacitor is connected to a 110 V, 60 Hz ac supply. What is the rms current? 2.49 A.
15 What is the quality factor of a series LCR circuit? \( Q = \frac{\omega_0 L}{R} \).
16 What is the instantaneous power supplied to a pure inductor? \( p_L = -\frac{i_m v_m}{2}\sin(2\omega t) \).
17 In the phasor diagram for a series LCR circuit, what is the phase relationship between \( \mathbf{V_R} \) and the current phasor \( \mathbf{I} \)? \( \mathbf{V_R} \) is parallel to (in phase with) \( \mathbf{I} \).
18 In a series LCR circuit, power is dissipated only in which element? The resistor (R).
19 Why is the algebraic sum of VR and VC (311.3 V) greater than the 220 V source voltage in Example 7.6, and how is this resolved? VR and VC are 90° out of phase and cannot be added algebraically; using the Pythagorean theorem, \( V_{RC}=\sqrt{V_R^2+V_C^2}=220 \) V, matching the source voltage.
20 How is flux leakage in a transformer reduced? By winding the primary and secondary coils one over the other.
21 When a value is quoted for ac voltage or current without qualification, which value is it? The rms value.
22 On what property is the definition of the ac ampere based? Joule heating — one ampere rms of alternating current produces the same average heating effect as one ampere of dc current under the same conditions.
23 How are the roles of input and output energy reversed between a motor and a generator? In a motor, electrical energy is the input and mechanical energy is the output; in a generator, mechanical energy is the input and electrical energy is the output.
24 NEET 2024 (Re-Exam): A step-up transformer runs on a 220 V ac mains supply to deliver 11000 V at 88 W. Ignoring losses, what is the current in the secondary circuit? 8 mA \( \left(I_s=\dfrac{P}{V_s}=\dfrac{88\,W}{11000\,V}\right) \).
25 George Westinghouse (1846–1914) was a leading proponent of alternating current — who did this put him in conflict with, and what did he do to advance ac? It put him in conflict with Thomas Alva Edison, an advocate of direct current. Westinghouse founded the company named after him and enlisted Nicola Tesla and other inventors to develop ac motors and high-tension transmission apparatus, pioneering large-scale lighting.
26 In the phasor diagram for a series LCR circuit, how do the capacitor and inductor voltage phasors \( \mathbf{V_C} \) and \( \mathbf{V_L} \) relate in phase to the current phasor \( \mathbf{I} \)? \( \mathbf{V_C} \) is \( \pi/2 \) behind \( \mathbf{I} \), and \( \mathbf{V_L} \) is \( \pi/2 \) ahead of \( \mathbf{I} \) — opposite to each other, which is why they can be combined into a single phasor \( (\mathbf{V_C}+\mathbf{V_L}) \) along the same line.
27 For that same resonating circuit (Exercise 7.8: L = 5.0 H, C = 80 μF, R = 40 Ω, 230 V rms, \( \omega_0=50 \) rad/s), what are the rms potential drops across R, L and C individually — and why is the drop across the LC combination zero despite each being far larger than the source voltage? \( V_R = I_{rms}R = 5.75\times40=230 \) V (equal to the source, since \( Z=R \)); \( V_L=I_{rms}X_L=5.75\times250\approx1437.5 \) V; \( V_C=I_{rms}X_C=5.75\times250\approx1437.5 \) V. \( V_L \) and \( V_C \) are equal in magnitude but \( \pi \) out of phase with each other, so they cancel exactly — the LC combination's net drop is zero even though each individually far exceeds the source voltage.
28 A 100 W lamp is run on a 200 V ac supply. Treating it as a pure resistor, what is the peak current through it? (NEET 2022, Phase 2) \( \approx0.707 \) A — from \( I_{rms}=P/V=100/200=0.5 \) A, and \( i_m=\sqrt2\,I_{rms} \).
29 A series LCR circuit is connected to an ac source. When L is removed, the phase difference between current and voltage is \( \pi/3 \). When C is removed instead, the phase difference is again \( \pi/3 \). What is the power factor of the original (LCR) circuit? (NEET 2020) 1.0 — removing L leaves an RC circuit with \( \tan(\pi/3)=X_C/R \), and removing C leaves an RL circuit with \( \tan(\pi/3)=X_L/R \); since both give the same ratio, \( X_C=X_L \), so the original circuit is at resonance: \( \phi=0 \) and \( \cos\phi=1 \).