Alternating Current

The formula to find the average (real) power in an AC circuit is:
P=V‌rms ‌×I‌rms ‌×cos‌φ where φ is the phase difference between voltage and current.
The voltage is 50sin‌(50t), so its maximum (peak) value is 50 V .
The current is 50sin‌(50t+‌

π

4

), so its peak value is 50mA=50×10−3A.
The phase difference φ between voltage and current is ‌

π

4

.
To get the RMS (root mean square) values from the peak values, divide by √2 :
‌Vrms=‌

50

√2

‌Irms=‌

50×10−3

√2

Now, put these values into the power formula:
‌P=‌

50

√2

×‌

50×10−3

√2

×cos(‌

π

4

)
‌cos(‌

π

4

)‌ is ‌‌

1

√2

.
So,
P=‌

50

√2

×‌

50

√2

×10−3×‌

1

√2

Multiply the numbers:
‌=‌

50×50×10−3

√2×√2×√2

‌√2×√2×√2=2√2
‌=‌

2500×10−3

2√2

‌=‌

2.5

2√2

This is approximately equal to 0.884 W .