Alternating CurrentHard

Question

The electric current in the circuit is given as $i = i_{o}(t/T)$. The r.m.s current for the period $t = 0$ to $t = T$ is $\_\_\_\_$

Options

A.$\frac{i_{0}}{\sqrt{2}}$
B.$i_{0}$
C.$\frac{i_{0}}{\sqrt{6}}$
D.$\frac{i_{0}}{\sqrt{3}}$

Solution

$i_{rms}^{2} = \frac{\int_{0}^{T}\mspace{2mu}\left( i_{0}^{2}t^{2}/T^{2} \right)dt}{\int_{0}^{T}\mspace{2mu} dt} = \frac{i_{0}^{2}}{{\text{ }T}^{3}} \cdot \frac{{\text{ }T}^{3}}{3} = \frac{i_{0}^{2}}{3}$

$$i_{\text{rms~}} = \frac{i_{0}}{\sqrt{3}}$$

Create a free account to view solution

View Solution Free
Topic: Alternating Current·Practice all Alternating Current questions

More Alternating Current Questions

In a circuit the current the coil of a choke :...In a series LCR circuit voltage across resister, induetor and capaceter are 1V, 3V and 2V respectively. At the instant t...Power factor of a best choke coil is :...L, C and R represent physical quantities inductance, capacitance and resistance respectively. The combination representi...What is true in L.C.R. series circuit at a frequency less than resonant frequency:-(a) I, lags E(b) Circuit nature &#859...