Question

If I_m is the maximum current, then the average value of power dissipated in a resistance R over a cycle is ______.

विकल्प

• `3/2 "I"_"m"^2 "R"`

• `1/2 "I"_"m"^2 "R"`

• `2 "I"_"m"^2 "R"`

• `"I"_"m"^2 "R"`

Answer 1

If I_m is the maximum current, then the average value of power dissipated in a resistance R over a cycle is `underline(1/2 "I"_"m"^2 "R")`.

Explanation:

In an AC circuit, the instantaneous electric power is provided by P = VI, just as it is in a DC circuit, but these quantities are constantly changing. As a result, the average power is

P_avg = VI cos`phi`

where `phi` is the phase angle between the current and the voltage, and V and I are the effective or rms voltage and current values, respectively.

Now, RMS value of I is = `"I"_"m"/sqrt2`

So, RMS value of V = `("I"_"m""R")/sqrt2`

Therefore, Power will be

P = `1/2 "I"_"m"^2"R"` (because cos Φ = 1 for circuit containing resistance only).