Answer:
Explanation:
Given that a coil has a turns of
N = 110 turns
And the flux is given as function of t
ΦB = 9.75 ✕ 10^-3 sin(ωt),
Given that, at an instant the angular velocity is 8.70 ✕ 10² rev/min
ω = 8.70 ✕ 10² rev/min
Converting this to rad/sec
1 rev = 2πrad
Then,
ω = 8.7 × 10² × 2π / 60
ω = 91.11 rad/s
Now, we want to find the induced EMF as a function of time
EMF is given as
ε = —NdΦB/dt
ΦB = 9.75 ✕ 10^-3 sin(ωt),
dΦB/dt = 9.75 × 10^-3•ω Cos(ωt)
So,
ε = —NdΦB/dt
ε = —110 × 9.75 × 10^-3•ω Cos(ωt)
Since ω = 91.11 rad/s
ε = —110 × 9.75 × 10^-3 ×91.11 Cos(91.11t)
ε = —97.71 Cos(91.11t)
The EMF as a function of time is
ε = —97.71 Cos(91.11t)
Extra
The maximum EMF will be when Cos(91.11t) = -1
Then, maximum emf = 97.71V
