How to calculate the resistivity of a trapezium ?

To calculate the resistivity of a trapezium, you will need to know the dimensions of the trapezium and the resistivity of the material it is made of.

1. First, calculate the area of the trapezium using the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides of the trapezium and h is the height of the trapezium.

2. Next, calculate the length of the trapezium using the formula:
Length = √(h^2 + ((b - a) / 2)^2)
where h is the height of the trapezium and a and b are the lengths of the parallel sides of the trapezium.

3. Finally, calculate the resistivity of the trapezium using the formula:
Resistivity = resistance * (Length / Area)
where resistance is the resistivity of the material the trapezium is made of.

By following these steps, you can calculate the resistivity of a trapezium.

Formula:

```
ρ = (2L / (b1 + b2)) - (V / I)
```

where:

- ρ is the resistivity in ohm-meters (Ω-m)
- L is the average length of the trapezium in meters (m)
- b1 and b2 are the lengths of the parallel sides of the trapezium in meters (m)
- V is the voltage applied across the trapezium in volts (V)
- I is the current flowing through the trapezium in amperes (A)

Calculation Steps:

1. Determine the average length (L):
- Calculate the average of the two parallel sides: (b1 + b2) / 2
- Multiply the average by 2 since the current flows through both parallel sides.

2. Apply the formula:
- Substitute the values of L, b1, b2, V, and I into the formula.
- Calculate the resistivity ρ in ohm-meters.

Example:

Consider a trapezium with:

- b1 = 5 cm = 0.05 m
- b2 = 7 cm = 0.07 m
- L = 10 cm = 0.1 m
- V = 12 V
- I = 2 A

Calculation:

1. Average length: (b1 + b2) / 2 = (0.05 m + 0.07 m) / 2 = 0.06 m
- L = 2 - 0.06 m = 0.12 m

2. Resistivity:
- ρ = (2 - 0.12 m / (0.05 m + 0.07 m)) - (12 V / 2 A)
- ρ = 0.03 Ω-m

Therefore, the resistivity of the trapezium is 0.03 Ω-m.