Consider a straight cylinder of length L. The two ends of the wire are held at different electric potentials so that the potential difference (or voltage) across the length of the wire is ΔV. For concreteness, assume the left end is at a higher potential.
1) Assuming the electric potential varies linearly across the length, compute the electric field in the wire and indicate its direction. Leave your answer in terms of ΔV and L.
2) The electric field you found would accelerate free charges (namely electrons) in the material and drive a current I = dQ/dt, which is the rate at which charge passes by a particular position along the cylinder. The electrons are, of course, not completely free, and their motion is affected by collisions with other particles (such as atoms). The extent to which electrons and hence current are impeded is characterized by the (usually experimentally measured) electrical resistance R of the material. Under certain conditions, many substances obey Ohm's Law: ΔV = IR. That is, the current I flowing through the material is proportional to the applied potential difference ΔV and decreases with increasing resistance R. Now imagine the cylinder is a resistor, a device whose resistance R is intentionally much higher than that of typical electrical wires in circuits. The figure below shows a circuit where a battery with a potential difference ΔV pushes charges into the wire and the resistor.
2) Starting with point A in the diagram, follow the circuit to move upwards. Upon encountering the battery, the electric potential increases by ΔV if we define the so-called conventional current to flow clockwise as indicated by the arrows along the circuit. If we follow the circuit back to point A, what must be the total change in electric potential ΔVtotal around the whole loop? Briefly explain your reasoning.
3) The wires in the circuit are conductors. In the idealized approximation that the wire resistance is negligible (effectively 0) compared to that of the resistor, what is the potential difference ΔVR across the resistor? You should get a simple answer that requires almost no calculation. Again, please briefly explain your reasoning.
A voltmeter is a device that measures the potential difference between two points while an ammeter measures the current flowing through it. That is, the current must come in through one of the ammeter leads and leaves through the other.
4) Redraw the circuit diagram and include a voltmeter to experimentally measure the potential difference (sometimes called voltage drop) between two ends of the resistor. Explain why the voltmeter must be connected in the manner that you have indicated.
5) Redraw the circuit diagram again but this time include an ammeter to experimentally measure the current flowing through the resistor. Explain why the ammeter must be connected in the manner that you have indicated. (Hint: How is the current through the resistor related to the current through the entire circuit?)