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

Answer:

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

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;

$I_{rms} = \frac{I_o}{\sqrt{2} }$

$P_{avg} = (\frac{I_o}{\sqrt{2} } )^2R\\\\P_{avg} = \frac{I_o^2R}{2} ----equation(1)$

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;

$I_d^2R = \frac{I_o^2R}{2} \\\\I_d^2 = \frac{I_o^2}{2} \\\\I_d=\sqrt{\frac{I_o^2}{2} } \\\\I_d = \frac{I_o}{\sqrt{2}} \\\\I_d = \frac{2.59}{\sqrt{2} } \\\\I_d = 1.83 \ A$

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