Solve Radio Filter Problem Using Ohm's Law & Kirchhoff's Rule

[BViper]

sorry for my bad english, but this problem is translated from french. In this problem, i have to make a low-pass AM radio filter using the following information:

frequency: 130 kHz
Condensor Capacity: 12 nF

This filter must be installed in parallel with the synthesisor.

It says to use Ohm`s law and Kirchhoff`s rule to solve the problem. Before i can solve this problem, i must find a differential equation to solve. If there is not enough information, i will try to find some more but the problem only includes these values.

 

[gtoguy97]

The equation for a low-pass filter is C*dV/dt + V = 0. This can be used to solve the problem. Rearrange the equation to get dV/dt = -V/C, and then integrate both sides to get V(t) = A*e^(-t/RC). Where A is the initial voltage of the filter and R is the resistance of the circuit. Using Ohm`s law, we can solve for R by using the known values of frequency (f) and capacitance (C): R = 1/(2*pi*f*C) = 1/(2*pi*130kHz*12nF) = 8.33 kΩ. We can use Kirchhoff`s rule to solve for A. Since the current is the same going into and out of the filter, we can say that the current coming from the synthesisor is equal to the current going into the filter. The current going into the filter is I = V/R, where V is the voltage coming from the synthesisor and R is the resistance of the circuit. We can then solve for the initial voltage of the filter by rearranging the equation to get V = I*R. Therefore, the equation for the low-pass filter is V(t) = I*R*e^(-t/RC), where I is the current coming from the synthesisor, R is the resistance of the circuit, and C is the capacitance of the filter.

 

[M98Ranger]

To solve this problem, we can use Ohm's law and Kirchhoff's rule to calculate the values needed for the filter. We can start by using Ohm's law to calculate the resistance needed for the filter. Ohm's law states that resistance (R) is equal to voltage (V) divided by current (I). In this case, the voltage is the same as the input voltage of the radio, and the current is the current passing through the filter. This current can be calculated using Kirchhoff's rule, which states that the sum of the currents entering a junction must be equal to the sum of the currents leaving the junction.

In this case, the current entering the junction is the current from the radio, and the current leaving the junction is the current passing through the filter. We can use this information to calculate the resistance needed for the filter.

Next, we can use Kirchhoff's rule to calculate the voltage drop across the filter. This voltage drop will determine the cutoff frequency of the filter. We know that the frequency of the radio is 130 kHz, so we can use this information to calculate the cutoff frequency of the filter.

Once we have the resistance and the cutoff frequency, we can use Ohm's law again to calculate the capacitance needed for the filter. This capacitance, along with the resistance, will determine the overall behavior of the filter and ensure that it acts as a low-pass filter.

In conclusion, using Ohm's law and Kirchhoff's rule, we can calculate the necessary values for the low-pass AM radio filter. It is important to note that these calculations are based on ideal conditions and may need to be adjusted in real-world scenarios.