Question

The phase difference between current and voltage in an AC circuit is π/4 radian. If the frequency of AC is 50Hz, then the phase difference is equivalent to the time difference?

Answer 1

Step 1: Given Data,

Phase Difference between current and voltage in an AC circuit =$\frac{\pi }{4}radian$

Frequency=$50Hz$

Step 2: Formula Used,

$\text{Time}\text{period =}{\displaystyle \frac{\text{1}}{\text{frequency}}}$.

Step 3: Calculating the Time Difference,

Frequency of the circuit is $50Hz$.
Therefore the time period of the wave is ${\displaystyle \frac{1}{f}}={\displaystyle \frac{1}{50}}=0.02s$

For one complete cycle $2\pi$ correspond to $T$
So for ${\displaystyle \frac{\pi }{4}}$ radian time period will be $\frac{T}{2\pi }\times \frac{\pi }{4}$

Here time period $T$ of the wave is $0.02sec$, Hence,

${\displaystyle \frac{0.02}{2\pi }}\text{x}{\displaystyle \frac{\pi }{4}}=0.0025s=2.5ms$.

Thus ${\displaystyle \frac{\pi }{4}}$ has the time period of 2.5ms