Question

(a) Current I(t)=I₀ cos(2πf·t) that oscillates with frequency f.

(b) Current I(t)=I₀e^−t/τ that decays in time with time constant τ.

Questions will be related to the currents with amplitude I₀=1.5 A running in the copper (resistivity ρ= 1.7  10^-8 Ω·m) wire of diameter d=3 mm and length l=0.68 m.

How much energy W_a is dissipated in the wire via Joule heating during one period of current oscillations for frequency f=50.8 Hz?:
W_a= ____ mJ.

With the oscillating current, the amount of charge passing through any cross-section of the wire would, of course, also oscillate with the same frequency. What is the amplitude Q₀ of charge oscillations?:
Q₀= ____ mC.

How much energy W_b is dissipated in the wire via Joule heating during the full decay of the current (from t=0 to t=∞) for time constant τ=23.94 ms?:
W_b= ____ mJ.

How much charge Q_b passes through any cross-section of the wire during the full decay of the current?:
Q_b= ____ mC.

Answer 1

Resistance of wire =

a) , [, f = 50.8 Hz]

i) Energy dissipated through R is

  

= 0.029 mJ [answer]

ii) Integrating Current with respect to time gives charge

Charge amplitude is =

[answer]

b) , [, ]

i) Energy dissipated through R is

= 0.043 mJ [answer]

ii) Total charge that passes in full decay is

= 0.03591C = 35.91mC [answer]