krit.club logo

Magnetic Effects of Electric Current - Frequency of AC

Grade 10CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Alternating Current (AC) is the electric current that reverses its direction periodically with time, unlike Direct Current (DC) which flows in only one direction.

•

The frequency of AC is the number of cycles completed by the current in one second. It is measured in Hertz (HzHz).

•

In India, the standard frequency of AC supply for domestic purposes is 50 Hz50 \text{ Hz}.

•

A frequency of 50 Hz50 \text{ Hz} means the current completes 5050 full cycles in one second.

•

Since the current reverses its direction twice in every cycle (once during the positive half and once during the negative half), AC with a frequency of 50 Hz50 \text{ Hz} changes its direction 100100 times in one second.

•

The time period (TT) is the time taken to complete one full cycle of the alternating current.

•

Direct Current (DC) has a frequency of 0 Hz0 \text{ Hz} because it does not change its direction over time.

📐Formulae

f=1Tf = \frac{1}{T}

T=1fT = \frac{1}{f}

Number of direction changes per second=2×f\text{Number of direction changes per second} = 2 \times f

💡Examples

Problem 1:

In India, the frequency of AC is 50 Hz50 \text{ Hz}. Calculate the time taken by the current to change its direction once.

Solution:

Given, frequency f=50 Hzf = 50 \text{ Hz}. The time period TT for one complete cycle is T=1f=150=0.02 sT = \frac{1}{f} = \frac{1}{50} = 0.02 \text{ s}. Since the current changes its direction twice in one cycle (at every half cycle), the time interval between direction changes is T2=0.022=0.01 s\frac{T}{2} = \frac{0.02}{2} = 0.01 \text{ s}.

Explanation:

In a 50 Hz50 \text{ Hz} supply, one full cycle takes 0.02 seconds0.02 \text{ seconds}. The current reaches its peak and returns to zero, then reverses direction; this reversal happens every half-cycle, which is 0.01 seconds0.01 \text{ seconds}.

Problem 2:

If an alternating current completes 6060 cycles in one second, what is its frequency and time period?

Solution:

Frequency f=60 Hzf = 60 \text{ Hz}. Time period T=1f=160≈0.0167 sT = \frac{1}{f} = \frac{1}{60} \approx 0.0167 \text{ s}.

Explanation:

Frequency is defined as the number of cycles per second. The time period is the reciprocal of the frequency.