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In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30?
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In the circuit shown below, the switch is closed at t = 0. The value o...
To determine the value of θ that will give the maximum value of DC offset of the current at the time of switching, we need to analyze the circuit and calculate the current through it.
1. **Circuit Analysis:**
- Given: R = 3.77 Ω, L = 10 mH, v(t) = 150 sin (377t + θ)
- The circuit consists of a resistor (R) and an inductor (L) connected in series.
- When the switch is closed at t = 0, the circuit becomes a DC circuit.
- The current through the circuit can be calculated using Ohm's Law and the properties of inductors.
2. **Calculating the DC Offset:**
- At DC, inductors behave like short circuits, and the current through them is constant.
- Therefore, the inductor can be replaced with a short circuit.
- The circuit now consists of a resistor (R) connected directly to the voltage source (v(t)).
- The current through the circuit can be calculated using Ohm's Law: I = V/R, where V is the voltage across the resistor.
- The voltage across the resistor is given by V = v(t) - V_offset, where V_offset is the DC offset of the voltage waveform.
- To find the maximum value of the DC offset, we need to find the maximum value of V_offset.
3. **Calculating the Maximum DC Offset:**
- The maximum value of V_offset occurs when the voltage waveform v(t) is at its peak.
- At the peak of a sine wave, the phase angle θ is either 90° or -90°.
- Plugging in θ = 90° into the voltage waveform equation, we get v(t) = 150 sin (377t + 90°).
- The maximum value of V_offset can be calculated by finding the difference between the peak value of v(t) and the average value of the waveform.
- The average value of a sine wave over one period is zero.
- Therefore, the maximum value of V_offset is equal to the peak value of v(t) when θ = 90°.
- Plugging in θ = 90° into the voltage waveform equation, we get v(t) = 150 sin (377t + 90°) = 150.
- Hence, the maximum value of the DC offset is 150V.
4. **Conclusion:**
- The value of θ in degrees that will give the maximum value of DC offset of the current at the time of switching is 90°.
- Therefore, the correct answer is option (C) 90.
1. **Circuit Analysis:**
- Given: R = 3.77 Ω, L = 10 mH, v(t) = 150 sin (377t + θ)
- The circuit consists of a resistor (R) and an inductor (L) connected in series.
- When the switch is closed at t = 0, the circuit becomes a DC circuit.
- The current through the circuit can be calculated using Ohm's Law and the properties of inductors.
2. **Calculating the DC Offset:**
- At DC, inductors behave like short circuits, and the current through them is constant.
- Therefore, the inductor can be replaced with a short circuit.
- The circuit now consists of a resistor (R) connected directly to the voltage source (v(t)).
- The current through the circuit can be calculated using Ohm's Law: I = V/R, where V is the voltage across the resistor.
- The voltage across the resistor is given by V = v(t) - V_offset, where V_offset is the DC offset of the voltage waveform.
- To find the maximum value of the DC offset, we need to find the maximum value of V_offset.
3. **Calculating the Maximum DC Offset:**
- The maximum value of V_offset occurs when the voltage waveform v(t) is at its peak.
- At the peak of a sine wave, the phase angle θ is either 90° or -90°.
- Plugging in θ = 90° into the voltage waveform equation, we get v(t) = 150 sin (377t + 90°).
- The maximum value of V_offset can be calculated by finding the difference between the peak value of v(t) and the average value of the waveform.
- The average value of a sine wave over one period is zero.
- Therefore, the maximum value of V_offset is equal to the peak value of v(t) when θ = 90°.
- Plugging in θ = 90° into the voltage waveform equation, we get v(t) = 150 sin (377t + 90°) = 150.
- Hence, the maximum value of the DC offset is 150V.
4. **Conclusion:**
- The value of θ in degrees that will give the maximum value of DC offset of the current at the time of switching is 90°.
- Therefore, the correct answer is option (C) 90.
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In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30?
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In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30?.
In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the circuit shown below, the switch is closed at t = 0. The value of θ in degrees which will give the maximum value of DC offset of the current at the time of switching is R=3.77 Ω L=10 mH AC (A) 60 t = 0 v(t)=150 sin (377t + θ) (B) −45 (C) 90 (D) −30?.
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