please help! A current loop with a resistance R = 463 ohm and an area A = 0.25 m
ID: 3893212 • Letter: P
Question
please help!
A current loop with a resistance R = 463 ohm and an area A = 0.25 m2 is oriented perpendicular to a magnetic field that varies in time as sketched in the figure. What is the current induced in the loop at t = 0.30 s? (Hint: You can express the magnetic field in the form B=B0sin(2pi f*t).) 1 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0 5 up to 10 attempts] What is the current induced in the loop at t = 0.50 s? 1 attempt(s) made (maximum allowed for credit = 5) [after that, multiply credit by 0 5 up to 10 attempts]Explanation / Answer
a)
B = Bo sin(2 pi f t)
dB/dt = (2*pi*f) * Bo cos (2 pi f t)
where Bo = Bmax = 0.5
since the sin wave completes 180 deg phase in 1s(from the diagram) , it makes 360 degree phase in 2 sec, so the time period is 2seconds.
this gives f = frequency = 1/(time period) = 0.5 Hz
so 2 pi f = 2 pi * 0.5 = pi
Hence dB/dt = pi * 0.5 * cos(2 * pi * 0.5 * 0.3) = 0.5 pi*cos(0.3 pi)
I (current) = (1/R) * area * dB/dt
= (1/463) * 0.25 * (0.5 * pi * cos (0.3 pi))
= 0.4985 mA
= 4.98E-4 Amperes
b) At t = 0.5
I (current) = (1/R) * area * dB/dt
= (1/463) * 0.25 * (0.5 * pi * cos (0.5 pi))
= 0
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