The individual pulse discharge energy (E_d) can be calculated using the formula:
E_d = 0.5 * C * V^2
where C is the capacitance and V is the voltage.
Since the duty factor is 0.5, the discharge time (t_d) is equal to the period (T) divided by 2:
t_d = T / 2 = 1 / (2 * f) = 1 / (2 * 6250) = 8 × 10^-5 s
The capacitance can be calculated using the formula:
C = I * t_d / (V - V_f)
where I is the current, V is the discharge voltage, and V_f is the forward voltage drop of the diode.
Assuming a diode forward voltage drop of 0.7 V, we can calculate the capacitance:
C = 80 * 8 × 10^-5 / (30 - 0.7) = 0.000281 F
Now we can calculate the individual pulse discharge energy:
E_d = 0.5 * C * V^2 = 0.5 * 0.000281 * 30^2 = 0.038 J
Therefore, the individual pulse discharge energy (E_d) is 0.038 J.