Answer:
96.10 A
Explanation:
The capacitor is connected to a voltage source defined by the expression,
V(t) = √2 × Vrms×sin2πft
Where V(t)=instantaneous voltage, Vrms= root mean square voltage value, f= frequency, t= time π=pi.
Vrms= 120 V, f= 60.0Hz, t= 1/171s, π= 3.143.
∴ V(t) = √2 × 120 × sin(2×3.143×60×t)
∴V(t) = 169.71 × sin(377.16t)............(1)
using capacitor's equation,
I(t)=C(dv/dt)...................(2)
Note: the differentiation of sin∅ = cos∅
∴ dv/dt=169.71×377.16×cos(377.16t)
dv/dt = 64109.65× cos(377.16t)
At time t=1/171s.
∴dv/dt=64109.65 × cos(377.16×1/171)
dv/dt = 64109.65 ×cos(2.21)
dv/dt = 64109.65 × 0.999
dv/dt = 64045.54.
I(t) = C(dv/dt)
Where C= I.5 mF = 0.0015 F
∴ I(t) = 0.0015 × 64045.54
I(t) = 96.07
I(t) ≈ 96.10 A
