Answer:
The unknown element is Capacitor.
Explanation:
The sinusoidal voltage is given as:
v(t) = V Sin (ωt + Ф)
Where:
V = Amplitude of Voltage
ω = 2π / T = > Time period (T)
Ф = phase shift
Considering no horizontal phase shift in the wave form, the equation can be written as:
v(t) = V Sin (ωt)--------(1)
Since, current in the capacitor can be given as:
i(t) = C dv(t)/dt = ωCV Cos (ωt)--------(2)
Now, checking all conditions:
At t=0 :
Equation (1) implies:
v(t) = V Sin [(2π/T)(0)] = V Sin (0)
v(t) = 0
The above finding satisfies the condition in the question. Now checking other conditions.
At t = T/4:
Equation (2) implies:
i(t) = ωCV Cos [(2π/T)(T/4)] = ωCV Cos [(π/2)] = ωCV (0)
i(t) = 0
At t = T/2 :
Equation (2) implies:
i(t) = ωCV Cos [(2π/T)(T/2)] = ωCV Cos [(π)] = ωCV (-1)
i(t) = - ωCV = max amplitude of current in negative direction
All three conditions of voltage and currents of question are satisfied with equations of capacitor hence, the unknown element is capacitor.
