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Calculate the peak value of the source voltage (in V) if the root-mean square voltage across the resistor and inductor in a series RL circuit is 13 V and 12 V, respectively. 
  • a)
    1
  • b)
    17.68
  • c)
    25
  • d)
    3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Calculate the peak value of the source voltage (in V) if the root-mean...
Calculation of Peak Value of Source Voltage:

Given:
- Root-mean square voltage across resistor (Vr) = 13 V
- Root-mean square voltage across inductor (Vl) = 12 V

Formula Used:
The root-mean square (RMS) voltage in a series RL circuit is given by:
Vrms = √(Vr^2 + Vl^2)

Calculation:
Given that Vrms = 13 V and 12 V for resistor and inductor respectively, we can substitute the values in the formula:
13 = √(Vr^2 + 12^2)
169 = Vr^2 + 144
Vr^2 = 169 - 144
Vr^2 = 25
Vr = 5 V
Now, to find the peak value of the source voltage (Vs), we use the relationship between peak, RMS, and peak-to-peak values:
Vs = √2 x Vrms
Substitute the RMS value of the source voltage into the formula:
Vs = √2 x 13
Vs = 13 x 1.414
Vs ≈ 18.38 V
Therefore, the peak value of the source voltage in the given series RL circuit is approximately 18.38 V.
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Community Answer
Calculate the peak value of the source voltage (in V) if the root-mean...
Concept:
Source voltage RMS value of a series RL circuit will be;
Vrms = √(VR2 + VL2)
Where;
Vrms → Source voltage in RMS.
VR  → Voltage across resistance in RMS.
VL  → Voltage across inductor in RMS.
RMS voltage = Peak voltage/√(2) 
Calculation:
Given;
VR = 13 V
VL  = 12 V
Vrms = √(VR2 + VL2) = √(132 + 122) = 17.69
Peak value of the source voltage = Vrms × √2 = 25.01 V ≈ 25 V
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