Answer :
Final Answer:
To design a filter with a capacitor of 1 μF that produces an output voltage of 2.24 V at 159 Hz with a 6 V input, we can use the formula for the voltage across a capacitor in an RC circuit: [tex]\( V_o = V_i \times \frac{1}{\sqrt{1 + (2\pi f R)^2}} \)[/tex]. Solving for R, we find [tex]\( R = \frac{1}{2 \pi f C} \)[/tex], where f is the frequency and C is the capacitance. Substituting the given values, [tex]\( R = \frac{1}{2 \pi \times 159 \times 1 \times 10^{-6}} \)[/tex].
Explanation:
To achieve the desired output voltage of 2.24 V at 159 Hz with a 6 V input using a capacitor of 1 μF, we need to calculate the resistance R required for the RC circuit.
By rearranging the formula for the voltage across a capacitor, we find that [tex]\( R = \frac{1}{2 \pi f C} \), where \( f \)[/tex] is the frequency and C is the capacitance.
Substituting the given values, we find the resistance R needed for the circuit. This calculated resistance value will ensure that the output voltage reaches the desired level at the specified frequency when the given input voltage is applied.
