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If a capacitor is connected to a voltage source with v (t) = 50 sin 2000t V, then the current through the capacitor is_____A.
- a)(106cos2000t)
- b)(5 x 10-4cos2000t )
- c)(cos2000t)
- d)(500cos2000t)
Correct answer is option 'C'. Can you explain this answer?
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If a capacitor is connected to a voltage source with v (t) = 50 sin 2...
Explanation:
The current through a capacitor is given by the formula:
i(t) = C(dv/dt)
where i(t) is the current at time t, C is the capacitance of the capacitor, and dv/dt is the rate of change of voltage with respect to time.
Given that v(t) = 50 sin 2000t V, we have:
dv/dt = 1000 cos 2000t V/s
Substituting the values of v(t) and dv/dt in the formula for i(t), we get:
i(t) = C(dv/dt) = C(1000 cos 2000t)
Since the options are in terms of cos 2000t, we can simplify i(t) as:
i(t) = 1000C cos 2000t A
Comparing this with the options, we see that the correct answer is option 'C':
i(t) = cos 2000t A
The current through a capacitor is given by the formula:
i(t) = C(dv/dt)
where i(t) is the current at time t, C is the capacitance of the capacitor, and dv/dt is the rate of change of voltage with respect to time.
Given that v(t) = 50 sin 2000t V, we have:
dv/dt = 1000 cos 2000t V/s
Substituting the values of v(t) and dv/dt in the formula for i(t), we get:
i(t) = C(dv/dt) = C(1000 cos 2000t)
Since the options are in terms of cos 2000t, we can simplify i(t) as:
i(t) = 1000C cos 2000t A
Comparing this with the options, we see that the correct answer is option 'C':
i(t) = cos 2000t A
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If a capacitor is connected to a voltage source with v (t) = 50 sin 2000t V, then the current through the capacitor is_____A.a)(106cos2000t)b)(5 x 10-4cos2000t )c)(cos2000t)d)(500cos2000t)Correct answer is option 'C'. Can you explain this answer?
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