Differentiate between peak and rms values of alternating current. How are
they related?
Solution and Explanation
Peak Value and RMS Value of Alternating Current
1. Peak Value (\( I_0 \))
The peak value of an alternating current (or voltage) is the maximum value attained in either direction during one cycle. It is also called the maximum value.
Definition: The highest point reached by the AC waveform during a cycle.
2. RMS Value (\( I_{\text{rms}} \))
The root mean square (rms) value of an alternating current is defined as the value of a steady (DC) current that would produce the same amount of heat in a given resistor in the same time as the AC does.
Mathematical Relation:
The RMS value for current is related to the peak value as:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
Similarly, for voltage, the RMS value is related to the peak voltage \( V_0 \) as:
\[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \]
Conclusion:
The RMS value is particularly useful because it represents the effective value of an alternating current or voltage, which can be directly compared to a DC value in terms of its ability to produce heat in a resistor.
Top Questions on Alternating current
- Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in figure. The energy stored in A is E. The energy stored in B, when spring constants \(k_A, k_B\) of A and B, respectively satisfy the relation \(4k_A = 3k_B\), is :
- JEE Main - 2026
- Physics
- Alternating current
- The electric current in the circuit is given as \[ i=i_0\left(\frac{t}{T}\right). \] The r.m.s. current for the period \( t=0 \) to \( t=T \) is:
- JEE Main - 2026
- Physics
- Alternating current
- For the series LCR circuit connected with $220\,\text{V},\,50\,\text{Hz}$ a.c. source as shown in the figure, the power factor is $\dfrac{\alpha}{10}$. The value of $\alpha$ is ___.
- JEE Main - 2026
- Physics
- Alternating current
- Find the energy density at the instant when the current is \( \dfrac{1}{e} \) times its maximum value. If the value obtained is \( \alpha \dfrac{\pi}{e^2} \), find \( \alpha \). Given: \[ \varepsilon = 10\,\text{V}, \quad R = 10\,\Omega, \quad L = 10\,\text{mH}, \quad \frac{N}{\ell} = 10000 \]
- JEE Main - 2026
- Physics
- Alternating current
- In the given L-C circuit, charge on the capacitor is maximum at \( t = 0 \), find the time at which charge becomes 25% of its initial value for the first time.
- JEE Main - 2026
- Physics
- Alternating current
Questions Asked in CBSE CLASS XII exam
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?
- Find the value of $x$, if \[ \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ x \\ 2 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \]
- Two point charges of \( -5\,\mu C \) and \( 2\,\mu C \) are located in free space at \( (-4\,\text{cm}, 0) \) and \( (6\,\text{cm}, 0) \) respectively.
(a) Calculate the amount of work done to separate the two charges at infinite distance.
(b) If this system of charges was initially kept in an electric field \[ \vec{E} = \frac{A}{r^2}, \text{ where } A = 8 \times 10^4\, \text{N}\,\text{C}^{-1}\,\text{m}^2, \] calculate the electrostatic potential energy of the system.- CBSE CLASS XII - 2025
- Electrostatics
- 4,000 shares of ₹ 10 each were forfeited for non-payment of second and final call money of ₹ 2 per share. The minimum amount that the company must collect at the time of reissue of these shares will be :
- CBSE CLASS XII - 2025
- Accounting for Share Capital
- If $y = a \cos(\log x) + b \sin(\log x)$, then $x^2y'' + xy'1$ is:
- CBSE CLASS XII - 2025
- Continuity and differentiability