Voltage and electric field in circuits

• proton
In summary, the conversation discusses the concept of potential difference and the relationship between voltage and EMF in a closed circuit with a single resistor. The voltage at point c is V1, increases by EMF to V2, and then decreases by IR to return to V1, implying that IR = EMF. The conversation also addresses the question of how deltaV can be zero but the electric field not be zero, and explains that the potential difference between points b and c is the integral of the electric field. The conclusion is that the limits of the integral are the same, resulting in a value of zero, but the electric field can still be nonzero.
proton
Let's say I have a closed circuit with 1 resistor. Let's say the EMF is between points c and a, the resistor between points a and b, and then between b and c there is nothing but the circuit wire. According to my textbook, the voltage at c is V1, increases by EMF to V2, where V2 = V1+EMF, and then V2 decreases by IR to return to V1 which implies that IR = EMF.

I understand all this. I understand that the voltage must return to V1 after completing the loop. But as you move along the wire where the voltage is a constant V1, deltaV must be 0 which implies that E must be 0 along the circuit path as deltaV is the work done by E. But since a current exists and is the same throughout the circuit, this implies that E must exist. So my question is how can deltaV be zero but the E not be 0?

It is becuase potential difference between the points b and c in this case is the integral of the electric field E:

$$V_b - V_c = \int_b ^c E \cdot d\mathbf{l}$$

What happens when we evaluate an integral whose limits are the same?

umm... b and c aren't the same points. The whole wire between b and c are at the same potential but the electric field between them is not 0.

umm... b and c aren't the same points. The whole wire between b and c are at the same potential but the electric field between them is not 0.
I did not say that b and c were the same points. If the whole wire between b and c is at the same potential, therefore Vb - Vc = 0. This means that Vb = Vc, hence the limits of the integral are the same.

if the limits are the same, that implies that the integral is 0, but E can still be nonzero as the limits are the same, right? I think I got it. Thanks a lot!

Yup, you've got got it. And you're welcome.

1. What is the difference between voltage and electric field in circuits?

Voltage refers to the potential difference between two points in a circuit, while electric field refers to the force that causes the movement of charges in a circuit. In other words, voltage is the cause of the electric field.

2. How are voltage and electric field related in a circuit?

Voltage and electric field are directly proportional in a circuit. This means that an increase in voltage will result in an increase in electric field, and vice versa.

3. How does the presence of a resistor affect voltage and electric field in a circuit?

A resistor resists the flow of electric current, which in turn decreases the voltage and electric field in a circuit. This is because the resistor reduces the amount of charge that can flow through the circuit, thus decreasing the electric field.

4. Can voltage and electric field be measured in a circuit?

Yes, voltage can be measured using a voltmeter and electric field can be measured using an electric field meter. Both of these devices can provide numerical values for voltage and electric field in a circuit.

5. How does the direction of the electric field affect the flow of charges in a circuit?

The direction of the electric field determines the direction in which charges will flow in a circuit. Charges will always flow from areas of high electric field to areas of low electric field.

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