Series circuit and total resistance

[UrbanXrisis]

In a series circuit, do large or small resistances have large or small voltage drops? If resistance is added to a seriese circuit, total resistance in the circiut increases right? If resistance is added to it, total current in the circiut decreses right?

 

[Chen]

As per Ohm's law:
$$V = IR$$
The larger the resistance, the bigger the potential drop is. Since the total resistance of resistors that are connected in series is:
$$R_T = R_1 + R_2 + ...$$
If you add more resistors in series, you increase the total resistance of the circuit. Since the total potential drop on all resistors must stay the same, the current decreases.

 

[UrbanXrisis]

Is that the same for a parallel connection? The larger the resistance, the larger the voltage drop? If they are the same, then larger the resistance, the smaller the current right? The General relationship for resistance in parallel circuit is R=R1+R2+R3...right?

 

[Chen]

No, that's in series connection. When connecting resistors in parallel the total resistance is:
$$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + ...$$
If you add more resistors, you can see that the right side of the equation grows, so the total resistance decreases. In parallel connection, the potential drop on all resistors is equal and isn't affected by their number or total resistance. Only the current changes when you add more resistors in parallel, or disconnect some.

 

[UrbanXrisis]

So in a parallel circuit, current decreases with more resistors correct?

For the general equations of volt and current in a series and parallel circuit, V=V1+V2+V3… and I=I1+I2+I3… right?

 

[Chen]

No, since more resistors equals less total resistance, the overall current increases as you add more resistors in parallel.

 

[UrbanXrisis]

Am I right that for the general equations of volt and current in a series and parallel circuit, V=V1+V2+V3… and I=I1+I2+I3…?

 

[Chen]

Yes, respectively.