Inductance and Instantaneous Current

[4Phreal]

Homework Statement

An inductor is connected to a 20.0-Hz sinusoidal power supply that produces a 50.0-V peak voltage. What inductance is needed to keep the instantaneous current in the circuit below 77.4 mA?

Homework Equations

X(L)min = V(rms)/I(rms)
I(rms) = I(max)/√2
X(L) = 2pi*f*L

The Attempt at a Solution

I(rms) = 77.4E-3 A / sqrt(2) = 0.0547300649 A
X(L)min = 50 V / 0.0547300649 A = 913.5746527 ohms
L = X(L)/(2pi*f) = 913.5746527 ohms / 2 / pi / 20 Hz = 7.27 Henry

But the answer is actually 5.14 Henry and I can't figure out why. Where did I go wrong?

 

[gneill]

The problem speaks about the instantaneous current value, so you'll want to deal with peak values rather than RMS ones.

 

[vela]

Or, equivalently, you didn't use the rms voltage when you calculated the reactance.