Answer:
t = 5.48 × 10⁻³ s
Explanation:
Given:
ΔV = ΔVmax × sin(2πft)
frequency, f = 16.9Hz
thus,
ΔV = ΔVmax × sin(2π×16.9×ft)
Now,
Let 'R' be the resistance
Also according to the ohms law
i = V/R
where,
i = current
V = voltage
hence,
[tex]i=\frac{\Delta V_{max}sin(2\pi \times 16.9\times t)}{R}[/tex]
also, given at time 't' the current in the circuit is 55.0% of the peak current
thus
[tex]i=\frac{55}{100}\times \frac{\Delta V_{max}}{R}=0.55\times \frac{\Delta V_{max}}{R}[/tex]
thus,
[tex]0.55\times \frac{\Delta V_{max}}{R}=\frac{\Delta V_{max}sin(2\pi \times 16.9\times t)}{R}[/tex]
or
[tex]0.55=sin(2\pi \times 16.9\times t)}[/tex]
or
[tex]0.5823=(2\pi \times 16.9\times t)}[/tex]
or
t = 5.48 × 10⁻³ s (Answer)
