## Related questions with answers

A series $R L$ circuit is often used as a low-pass filter. Consider a resistor $R$ and inductor $L$ connected in series to an oscillating source of emf with amplitude $\mathcal{E}_{\text {max }}$. In terms of $\mathcal{E}_{\text {max }}$, what is the amplitude of the voltage across the resistor for a low frequency, when $\omega L / R=1 / 10$ ? For a high frequency, when $\omega L / R=10$ ? At what frequency is the amplitude of the voltage across the resistor equal to $\mathcal{E}_{\max } / \sqrt{2}$ ?

Solution

VerifiedIn this problem, an RL circuit used as a low-pass filter is connected in series to a source with an amplitude of $\mathcal{E}_\text{max}$. Our objective is to determine the amplitude of the voltage across the resistor when $\omega L/R = 1/10$, and when $\omega L/R = 10$. Also, we want to determine the frequency where in the amplitude of the voltage across the resistor is $\mathcal{E}/\sqrt{2}$.

To solve the desired parameters in this problem, we will have to use the formula for the reactance of a capacitor :

$X_L = \omega L \tag{1}$

Also, we can solve for the amplitude of the voltage across the resistor by applying voltage division:

$V_\text{R,max} = \frac{R}{\sqrt{R^2+ {X_L}^2}} \mathcal{E}_\text{max} \tag{2}$

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