# The relationship between current and resistance

How electrical charge relates to voltage, current, and resistance. a quick way to reference the relationship between voltage, current, resistance, and power. Did you know that electrical current is affected by the voltage and resistance in a circuit? In this lesson, we'll use Ohm's law, which tells us how current, voltage, and resistance are related, as we work through several electric circuit examples. This equation, i = v/r, tells us. Find out about charge, resistance and ohms law with BBC Bitesize. Ohm's Law, shows the relationship between potential difference, current and resistance.

## Current and Resistance

When the circuit is completed, the entire charge distribution responds almost immediately to the electric field and is set in motion almost simultaneously, even though individual charges move slowly.

The battery provides a voltage V between its terminals. The electric field set up in a wire connected to the battery terminals causes the current to flow, which occurs when the current has a complete conducting path from one terminal of the batter to the other—called a circuit. By convention, the direction of current in the external circuit not in the battery is the direction of motion of positive charges.

In metals, the electrons are the moving charges, so the definition of the direction of current is opposite the actual flow of the negative charges in a wire. Electric fields are not found in conductors with static charges as shown by Gauss's law, but electric fields can exist in a conductor when charges are in motion.

The potential difference between the terminals of the battery when no current is present is called the electromotive force emf. The historical term emf is a misnomer because it is measured in volts, not force units, but the terminology is still commonly used.

Resistance and resistivity Experimentally, it was found that current is proportional to voltage for conductors. The proportionality constant is the resistance in the circuit. This relationship is called Ohm's law: Resistance is measured in ohms W: The resistivity for a specific conductor can be found in a table of properties of materials.

Resistance to current in a conductor arises because the flow of moving charges is impeded by the material of the wire. The relationship between resistance and resistivity is Note: The following equation gives the total cost of operating something electrical: Try this at home - figure out the monthly cost of using a particular appliance you use every day.

Possibilities include hair dryers, microwaves, TV's, etc. The power rating of an appliance like a TV is usually written on the back, and if it doesn't give the power it should give the current. Anything you plug into a wall socket runs at V, so if you know that and the current you can figure out how much power it uses.

The cost for power that comes from a wall socket is relatively cheap. On the other hand, the cost of battery power is much higher.

Although power is cheap, it is not limitless. Electricity use continues to increase, so it is important to use energy more efficiently to offset consumption. Appliances that use energy most efficiently sometimes cost more but in the long run, when the energy savings are accounted for, they can end up being the cheaper alternative. Direct current DC vs.

### Current and resistance

If the circuit has capacitors, which store charge, the current may not be constant, but it will still flow in one direction. The current that comes from a wall socket, on the other hand, is alternating current. With alternating current, the current continually changes direction.

This is because the voltage emf is following a sine wave oscillation. For a wall socket in North America, the voltage changes from positive to negative and back again 60 times each second. You might think this value of V should really be - volts. That's actually a kind of average of the voltage, but the peak really is about V.

This oscillating voltage produces an oscillating electric field; the electrons respond to this oscillating field and oscillate back and forth, producing an oscillating current in the circuit. The graph above shows voltage as a function of time, but it could just as well show current as a function of time: Root mean square This average value we use for the voltage from a wall socket is known as the root mean square, or rms, average.

Because the voltage varies sinusoidally, with as much positive as negative, doing a straight average would get you zero for the average voltage.

The rms value, however, is obtained in this way: To find the rms average, you square everything to get 1, 1, 9, and Finally, take the square root to get 3. The average is 2, but the rms average is 3. Doing this for a sine wave gets you an rms average that is the peak value of the sine wave divided by the square root of two. This is the same as multiplying by 0. If you need to know about the average power used, it is the rms values that go into the calculation.

Series circuits A series circuit is a circuit in which resistors are arranged in a chain, so the current has only one path to take. The current is the same through each resistor. The total resistance of the circuit is found by simply adding up the resistance values of the individual resistors: A series circuit is shown in the diagram above. The current flows through each resistor in turn. If the values of the three resistors are: The current through each resistor would be 0. Parallel circuits A parallel circuit is a circuit in which the resistors are arranged with their heads connected together, and their tails connected together.

### Current and Resistance

The current in a parallel circuit breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. The voltage across each resistor in parallel is the same.

The total resistance of a set of resistors in parallel is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total: A parallel circuit is shown in the diagram above. In this case the current supplied by the battery splits up, and the amount going through each resistor depends on the resistance.

The voltage across each resistor is 10 V, so: A parallel resistor short-cut If the resistors in parallel are identical, it can be very easy to work out the equivalent resistance.