The generator in a purely inductive AC circuit has an angular frequency of 553 rad/s. If the maximum voltage is 222 V and the inductance is 0.102 H, what is the rms current in the circuit? Answer in units of A

The rms current is 2.78 A

Explanation:

Given;

angular frequency, ω = 553 rad/s

maximum voltage, V₀ = 222 V

inductance, L = 0.102 H

The inductive reactance is given by;

The root mean square voltage is given by;

The rms current is given by;

Therefore, the rms current is 2.78 A

21420 J

Explanation:

Given that:

mass of the rider = 70 kg

the tension of the rope = 350 N

Using the concept of conservation of energy;

Work done = change in the Total energy ( ΔT.E)

where;

Work done (W) = ΔK.E + ΔP.E + ΔThermal Energy

Recall that the man proceeds with a constant speed, thus the change in K.E energy will be zero.

As such:

W  = ΔP.E + ΔThermal Energy

We can now say that:

The thermal energy = W - ΔP.E

here;

W = force × displacement

The thermal energy = (350 × 120) - (70 × 9.8 × 30)

= 42000 - 20580

= 21420 J