Question

In an ac circuit R = 4cm ,Z = 5 ohm ,Vrms = 200V & Irms = 1.5 A. Find average power consumed over a full cycle.

a. 200 V

b. 220 W

c. 240 W

d. 260 W
​

Answer 1

Solution :-

• Resistance = R = 4 Ω
• Impedance = Z = 5 Ω
• V rms = 200 V
• I rms = 1.5 A

We need to find the average power consumed over a full cycle ,

As per the formula ,

$\longrightarrow\mathtt{P_{avg }= V_{rms} I_{rms} cos\phi}$

we know that ,

$\longrightarrow\mathtt{ cos\phi= \dfrac{R}{Z}}$

Now let's substitute the given values in the above equation ,

$\longrightarrow\mathtt{ cos\phi= \dfrac{4}{5}}$

Hence ,

$\longrightarrow\mathtt{P_{avg} = 200 \times 1.5 \times \dfrac{4}{5}}$

$\longrightarrow\mathtt{P_{avg }= 200 \times 0.3 \times 4}$

$\longrightarrow\boxed{\mathtt{P_{avg }= 240 W}}$

The average power consumed over a full cycle is 240 W

Answer 2

$\huge \: ANsWeR :-$

P average =Vrms.Irms.cosθ

=Vrms.Irms.R/z

= 200 × 1.5 × 4/5

P average = 240 W

hence option C is correct answer ✅