• Is this the best solution?

It can be a viable solution, but the effectiveness will depend on the exact specifications of your stereo system and the duration of the power loss during switching. The capacitor would need to supply power long enough to cover the switching time, and have enough capacitance to supply the necessary current without the voltage dropping too much.

What type of capacitor should I use? 

You would likely want to use an electrolytic capacitor because they can provide a high capacitance in a small package and they are suitable for low-frequency (DC) applications like this.

The necessary capacitance can be roughly estimated by first determining the amount of charge (Q) needed. This can be calculated from the power (P) of the stereo and the time (t) of the power interruption as follows:

Q = P * t

Assuming the power interruption is very brief (say, 0.1 seconds), and the stereo is a 50W system running at 12V (which gives a current of about 4.2A), the required charge would be:

Q = 50W * 0.1s = 5 Joules

The energy stored in a capacitor can be calculated as:

E = 0.5 * C * V^2

Rearranging for C gives:

C = 2E / V^2

Substituting the values:

C = 2 * 5J / (12V)^2 = 0.07 Farads or 70,000 microFarads

So, a capacitor of around 70,000 microFarads (uF) and rated for at least 15V (preferably more for safety margin) should suffice.

• Would any other modifications to the circuit be a good idea? e.g. Should I worry about a flyback diode?

Including a flyback diode could be a good idea to prevent any potential reverse voltage spikes which could occur when the relay is switched off. This is particularly important if you have other sensitive electronics connected to the same circuit.

Is this the best solution?

It can be a viable solution, but the effectiveness will depend on the exact specifications of your stereo system and the duration of the power loss during switching. The capacitor would need to supply power long enough to cover the switching time, and have enough capacitance to supply the necessary current without the voltage dropping too much.

What type of capacitor should I use?

You would likely want to use an electrolytic capacitor because they can provide a high capacitance in a small package and they are suitable for low-frequency (DC) applications like this.

The necessary capacitance can be roughly estimated by first determining the amount of charge (Q) needed. This can be calculated from the power (P) of the stereo and the time (t) of the power interruption as follows:

Q = P * t

Assuming the power interruption is very brief (say, 0.1 seconds), and the stereo is a 50W system running at 12V (which gives a current of about 4.2A), the required charge would be:

Q = 50W * 0.1s = 5 Joules

The energy stored in a capacitor can be calculated as:

E = 0.5 * C * V^2

Rearranging for C gives:

C = 2E / V^2

Substituting the values:

C = 2 * 5J / (12V)^2 = 0.07 Farads or 70,000 microFarads

So, a capacitor of around 70,000 microFarads (uF) and rated for at least 15V (preferably more for safety margin) should suffice.

Would any other modifications to the circuit be a good idea? e.g. Should I worry about a flyback diode?

Including a flyback diode could be a good idea to prevent any potential reverse voltage spikes which could occur when the relay is switched off. This is particularly important if you have other sensitive electronics connected to the same circuit.

Adding a capacitor to the circuit could indeed help maintain power during the brief moment when you're switching between batteries. This approach is often referred to as a "capacitor hold up" circuit. The capacitor acts as a temporary power source that can fill in the gap while the power is being switched.

Is this the best solution? 

It can be a viable solution, but the effectiveness will depend on the exact specifications of your stereo system and the duration of the power loss during switching. The capacitor would need to supply power long enough to cover the switching time, and have enough capacitance to supply the necessary current without the voltage dropping too much.

What type of capacitor should I use? 

You would likely want to use an electrolytic capacitor because they can provide a high capacitance in a small package and they are suitable for low-frequency (DC) applications like this.

The necessary capacitance can be roughly estimated by first determining the amount of charge (Q) needed. This can be calculated from the power (P) of the stereo and the time (t) of the power interruption as follows:

Q = P * t

Assuming the power interruption is very brief (say, 0.1 seconds), and the stereo is a 50W system running at 12V (which gives a current of about 4.2A), the required charge would be:

Q = 50W * 0.1s = 5 Joules

The energy stored in a capacitor can be calculated as:

E = 0.5 * C * V^2

Rearranging for C gives:

C = 2E / V^2

Substituting the values:

C = 2 * 5J / (12V)^2 = 0.07 Farads or 70,000 microFarads

So, a capacitor of around 70,000 microFarads (uF) and rated for at least 15V (preferably more for safety margin) should suffice.

• Would any other modifications to the circuit be a good idea? e.g. Should I worry about a flyback diode?

Including a flyback diode could be a good idea to prevent any potential reverse voltage spikes which could occur when the relay is switched off. This is particularly important if you have other sensitive electronics connected to the same circuit.

Please note, this is a rough estimation and the actual requirements may vary. Always ensure any modifications to the electrical system of your vehicle are carried out safely, and if in doubt, consult with a professional electrician or auto mechanic.

• Is this the best solution?

It can be a viable solution, but the effectiveness will depend on the exact specifications of your stereo system and the duration of the power loss during switching. The capacitor would need to supply power long enough to cover the switching time, and have enough capacitance to supply the necessary current without the voltage dropping too much.

What type of capacitor should I use? 

You would likely want to use an electrolytic capacitor because they can provide a high capacitance in a small package and they are suitable for low-frequency (DC) applications like this.

The necessary capacitance can be roughly estimated by first determining the amount of charge (Q) needed. This can be calculated from the power (P) of the stereo and the time (t) of the power interruption as follows:

Q = P * t

Assuming the power interruption is very brief (say, 0.1 seconds), and the stereo is a 50W system running at 12V (which gives a current of about 4.2A), the required charge would be:

Q = 50W * 0.1s = 5 Joules

The energy stored in a capacitor can be calculated as:

E = 0.5 * C * V^2

Rearranging for C gives:

C = 2E / V^2

Substituting the values:

C = 2 * 5J / (12V)^2 = 0.07 Farads or 70,000 microFarads

So, a capacitor of around 70,000 microFarads (uF) and rated for at least 15V (preferably more for safety margin) should suffice.

• Would any other modifications to the circuit be a good idea? e.g. Should I worry about a flyback diode?

Including a flyback diode could be a good idea to prevent any potential reverse voltage spikes which could occur when the relay is switched off. This is particularly important if you have other sensitive electronics connected to the same circuit.