What happens to the voltage across each resistor?

[MIA6]

There is a diagram for this question, but I can't post it, so I just describe it. There are four resistors R1,R2,R3,R4. When the switch S is opened, current only flows through R1,R3 and R4. R3 and R4 are parallel to each other, but in series with R1. Now the switch is closed, what happens to the voltage across each resistor?
My solution is first to find out the current flows before and after the switch is closed through each resistor. I redrew the circuit into two circuits in series. First one is when switch is opened (R1,R34--I combined R3,R4 in parallel), the second one is when switch is closed (R1,R234--combined R2 with R34). Then I figured out that R234 < R34. Since V=IR. Now I am looking for the change in current before and after. My teacher told me current after the S is closed is bigger than the current when the S is opened? BUt is that because when you add more resistance to the circut, the current through the circuit will decrease? which in this case R234<R34, that's why I is more when the switch is closed?

Thanks.

 

[jbsteele]

Yes, when you add more resistance to a circuit, the current through the circuit will decrease, so when the switch is closed, the current will be larger than when the switch is open. This means that the voltage across each resistor will increase when the switch is closed.

 

[Moetasim]

I would like to provide a more comprehensive explanation for the voltage changes across each resistor in this circuit. Let's start by understanding the basics of voltage and resistance. Voltage is the potential difference between two points in a circuit, and it is measured in volts. Resistance is the opposition to the flow of electric current, and it is measured in ohms.

In this circuit, we have four resistors: R1, R2, R3, and R4. When the switch S is opened, current flows only through R1, R3, and R4. R3 and R4 are in parallel with each other, which means they have the same voltage across them. However, they are in series with R1, which means the voltage across R1 will be different from the voltage across R3 and R4.

Now, when the switch is closed, the circuit changes. R2 is now added in series with R3 and R4, creating a new effective resistance (R234) for this part of the circuit. This means that the current flowing through R3 and R4 will decrease, as the overall resistance has increased. However, the voltage across R3 and R4 will remain the same, as they are still in parallel with each other.

In terms of the voltage across R1, it will also remain the same when the switch is closed. This is because R1 is still in series with the rest of the circuit, and the total voltage across the series circuit must be the same. So, the voltage across R1 will not change, but the current flowing through it will decrease as the overall resistance of the circuit has increased.

In conclusion, the voltage across each resistor will remain the same when the switch is closed, except for R3 and R4 which are in parallel and will have the same voltage across them. The current flowing through each resistor will change, with R3 and R4 having a decrease in current due to the addition of R2 in series. This is in accordance with Ohm's Law, which states that the current through a resistor is inversely proportional to the resistance.