# Relationship between cross sectional area and resistance How the Resistance of a Wire is affected by Cross-Sectional Area This causes more collisions between the electrons and the atoms as, the atoms are moving. The resistance of a wire is inversely proportional to its cross-sectional area. Doubling the cross-sectional area of a wire will halve its resistance. Consider a uniform wire of cross-sectional area \$A\$ and length \$L\$ made of some conducting material. Suppose that the potential difference between the two .

Use the widget below to determine the resistance value from the colored stripes. Check Your Understanding 1. Household circuits are often wired with two different widths of wires: Thus, gauge wire has a wider cross section than gauge wire. A Amp circuit used for wall receptacles should be wired using gauge wire and a Amp circuit used for lighting and fan circuits should be wired using gauge wire. Explain the physics behind such an electrical code. See Answer A gauge wire is wider than gauge wire and thus has less resistance. The lesser resistance of gauge wire means that it can allow charge to flow through it at a greater rate - that is, allow a larger current. Thus, gauge wire is used in circuits which are protected by Amp fuses and circuit breakers. On the other hand, the thinner gauge wire can support less current owing to its larger resistance; it is used in circuits which are protected by Amp fuses and circuit breakers. Thus if two pairs of wires of the same material and length and of different cross section areas are tested at room temperature, using a circuit consisting of a battery eliminator and ampmeter, the wire with the lesser cross section area will give greater resistance when compared to the wire with larger cross section area.

Variations in this result in a difference in the spendant variables Room Temperature: Is the input that the battery eliminator will give. Calculated using voltage and current. Therefore, the length and material of the wire, as well as the temperature of the environment the experiment is conducted are controlled. The output ftom the battery eliminator is controlled manually, however it will give a fixed amount of voltage, enabling me to caluculate resistancem therefore battery eliminator output is controlled.

In order to have fair test, it is also important that the instruments used remain the same for the entrie course of the emperiment because other instruments may have an error which must then be checked everytime. Hence, the instruments used will not change and will remain controlled for the entrie experiment. Table of materials with quantity and their function.

## Electrical resistance and conductance

Material Quantity Function Battery Eliminator 1 Provides circuit with charge, eliminating higher current. Ammeter 1 Measures current flowing through wires of the circuit Voltmeter 1 Measures potential difference voltage throughout the circuit Copper Wires of cross sectional 2 To be used as the electricity area 0.

Using wires of cross sectional area 0. However, in order for fair test, I will have to ensure that the following factors are in order: Gather all material required for experiment. In order to verify the cross section area of both wires, measure diameter of each wire using a vernier calliper Step 3: Using formula for area of a circle calculate the cross sectional area for both wires.

Check with printed cross sectional areas on wires. Confirm accuracy in order to proceed. Using scissors cut wire of cross sectional area 0. Do the same with the wire of cross sectional area 0. In order to check for error in battery eliminator output, assemble a circuit using copper wires cross sectional area: Make sure that the wires connect from positive terminal to positive and negative terminal to negative. Changeand increase battery output, simulteniously recording voltmeter readings at every change. Replace voltmeter with ammeter. Ensure wires connected and ciruit are in normal conditions not heated up, not disconnected Step Ensure that wires are connected correctly; positive terminal to positive and negative terminal to negative.

Aishwarya Moothan Step Change and gradually increase the battery eliminator output while simulteniously recording the ammeter readings resultant of the battery output. Assemble a similar circuit,this time replacing wire of cross sectional area 0. Repeat steps 7 through 10 for second set of wires Step Calculate average resistance for both wires. Basic Circuit with ammeter and voltmeter Diagram 1.

### Electrical resistance and conductance - Wikipedia

Circuit when checking charge output from battery Physics Investigation: Aishwarya Moothan Diagram 1. Circuit when measuring current in wires of cross sectional area 0. A V-I Characteristics Graph Here the slope or gradient of the red line will give us the resistance of the conductor the V-I characteristics graphwas charted for. Aishwarya Moothan Table 1.

We can observe how the potential difference voltage is proportional to the current passing through it. In the hydraulic analogycurrent flowing through a wire or resistor is like water flowing through a pipe, and the voltage drop across the wire is like the pressure drop that pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow.

Conductance and resistance are reciprocals. The voltage drop i.

### Resistance and Resistivity

In hydraulics, it is similar: The pressure difference between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe.

But there may be an equally large water pressure below the pipe, which tries to push water back up through the pipe. If these pressures are equal, no water flows. In the image at right, the water pressure below the pipe is zero.

The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties: In the same way, a long, thin copper wire has higher resistance lower conductance than a short, thick copper wire. Materials are important as well.

A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. Similarly, electrons can flow freely and easily through a copper wire, but cannot flow as easily through a steel wire of the same shape and size, and they essentially cannot flow at all through an insulator like rubberregardless of its shape.

The difference between copper, steel, and rubber is related to their microscopic structure and electron configurationand is quantified by a property called resistivity.