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Consider the circuit shown in the figure with input V(t) in volts. The sinusoidal steady state current I(t) flowing through the circuit is shown graphically (where ? is in seconds). The circuit element ? can be
- a)a capacitor of 1 F
- b)an inductor of √3 H
- c)a capacitor of √3 F
- d)an inductor of 1 H
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider the circuit shown in the figure with input V(t) in volts. Th...
Given circuit and the waveform of sinusoidal steady state current I(t) is shown below,
Method 1
From the waveform of current I(t) , the current is lagging with respect to supply voltage V(t), because at
t = 0, V(t) is 0 and t = π/4, I(t) is 0.
Hence, the circuit element Z is inductor.
Thus, Z = jXL
Peak value of current I(t) = 1/√2 A
Peak value of voltage V(t) = 1V
Therefore impedance of circuit,
Since, XL = ωL
ωL = 1
Here ω = 1 rad/sec
L = 1H
Hence, the correct option is (D).
Method 2
Using sinusoidal steady state analysis :
Given : V(t) = sint , ω = 1 rad/sec
The given waveform of current I(t) and voltage V(t) is shown below,
From above figure it is clear that current,
it shows I(t) lags from voltage V(t) by an angle of π/4 it mean given circuit offer lagging power factor that’s why Z must be inductive reactance.
it shows I(t) lags from voltage V(t) by an angle of π/4 it mean given circuit offer lagging power factor that’s why Z must be inductive reactance.Thus, Z = jωL so equation (i) becomes as,
If L = 1H, then and only then,
Hence, the correct option is (D).
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Community Answer
Consider the circuit shown in the figure with input V(t) in volts. Th...
Given circuit and the waveform of sinusoidal steady state current I(t) is shown below,
Method 1
From the waveform of current I(t) , the current is lagging with respect to supply voltage V(t), because at
t = 0, V(t) is 0 and t = π/4, I(t) is 0.
Hence, the circuit element Z is inductor.
Thus, Z = jXL
Peak value of current I(t) = 1/√2 A
Peak value of voltage V(t) = 1V
Therefore impedance of circuit,
Since, XL = ωL
ωL = 1
Here ω = 1 rad/sec
L = 1H
Hence, the correct option is (D).
Method 2
Using sinusoidal steady state analysis :
Given : V(t) = sint , ω = 1 rad/sec
The given waveform of current I(t) and voltage V(t) is shown below,
From above figure it is clear that current, it shows I(t) lags from voltage V(t) by an angle of π/4 it mean given circuit offer lagging power factor that’s why Z must be inductive reactance.
it shows I(t) lags from voltage V(t) by an angle of π/4 it mean given circuit offer lagging power factor that’s why Z must be inductive reactance.Thus, Z = jωL so equation (i) becomes as,
If L = 1H, then and only then,
Hence, the correct option is (D).
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Consider the circuit shown in the figure with input V(t) in volts. The sinusoidal steady state current I(t) flowing through the circuit is shown graphically (where ? is in seconds). The circuit element ? can be a)a capacitor of 1 Fb)an inductor of √3 Hc)a capacitor of √3 Fd)an inductor of 1 HCorrect answer is option 'D'. Can you explain this answer?
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