Question

In the given circuit the average power developed is–

• A. 50 $\sqrt { 2 }$ watt
• B. 200 watt
• C. 150 $\sqrt { 2 }$ watt
• D. 200 $\sqrt { 2 }$ watt

Answer 1

Answer: (B)

200 watt

Answer 2

P = V_rms I_rms cosf

P = V_rms $\frac { V _ { \mathrm { rms } } } { Z }$ $\frac { \mathrm { R } } { \mathrm { Z } }$

= R

Z = $\sqrt { \mathrm { R } ^ { 2 } + ( \mathrm { L } \omega ) ^ { 2 } }$ = $\sqrt { ( 50 ) ^ { 2 } + ( 0.2 \times 250 ) ^ { 2 } }$

= $\sqrt { 2500 + ( 50 ) ^ { 2 } }$= 50 $\sqrt { 2 }$

P = $\left( \frac { 200 } { \sqrt { 2 } } \right) ^ { 2 }$ × $\frac { 1 } { 50 \sqrt { 2 } }$

= 200 watt