Question

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.59 A?

Answer 1

The direct current that will produce the same amount of thermal energy is 1.83 A

Step-by-step explanation:

Given;

maximum current, I₀ = 2.59 A

The average power dissipated in a resistor connected in an AC source is given as;

`P_(avg) = I_(rms) ^2R`

Where;

`I_(rms) = (I_o)/(√(2) )`

`P_(avg) = ((I_o)/(√(2) ) )^2R\\\\P_(avg) = (I_o^2R)/(2) ----equation(1)`

The average power dissipated in a resistor connected in a DC source is given as;

`P_(avg) = I_d^2R --------equation(2)`

where;

`I_d` is direct current

Solve equation (1) and (2) together;

`I_d^2R = (I_o^2R)/(2) \\\\I_d^2 = (I_o^2)/(2) \\\\I_d=\sqrt{(I_o^2)/(2) } \\\\I_d = (I_o)/(√(2)) \\\\I_d = (2.59)/(√(2) ) \\\\I_d = 1.83 \ A`

Therefore, the direct current that will produce the same amount of thermal energy is 1.83 A