The dimensional formula of Resistance is

**[ M**^{1}** L**^{2}** T**^{-3}** A**^{-2}**]**

where **[M]**, **[L],** **[T]**, and **[A]** are the fundamental quantities: **Mass**, **Length**, **Time**, and **Ampere**.

From the above formula, the **dimensions of resistance are (1, 2, -3, -2)**.

## How to calculate the dimensional formula of resistance?

We can use Ohm’s law to calculate the dimensional formula of resistance. the mathematic formula of Ohm’s law is

```
Voltage (V) = Current (I) * Resistance (R)
Resistance (R) = Voltage / Current
```

Now, let’s perform the breakdown of this formula in terms of fundamental quantities:

```
Voltage = Work / Charge
```

Replacing the value of **Work with Force * displacement**,

```
Voltage = (Force * displacement) / Charge
```

Replacing the value of **Force with mass * acceleration**,

```
Voltage = (mass * acceleration * displacement) / Charge
```

Also,

- acceleration = speed / time
- speed = distance / time
- acceleration = distance / time
^{2}

```
Voltage = (mass * distance / time
```^{2} * displacement) / ChargeĀ
= (mass * distance * displacement) / (Charge * time^{2})

Now, the formula of resistance becomes

```
Resistance = (mass * distance * displacement) / (Charge * Current * time
```^{2})

Also, the formula of **Charge is Current * time**. Hence, the formula becomes

```
Resistance = (mass * distance * displacement) / (Current * time * Current * time
```^{2})
= (mass * distance * displacement) / (Current^{2} * time^{3})
= (mass * distance * displacement * time^{-3} * Current^{-2})

Dimensionally, we use

**[M]**for mass**[L]**to represent both distance and displacement**[T]**for time- and
**[A]**for current

Now, the formula becomes

```
Resistance = [M
```^{1}] * [L^{2}] * [T^{-3}] * [A^{-2}]

Hence, the **dimensional equation of Resistance is R = [ M**^{1}** L**^{2}** T**^{-3}** A**^{-2}**]**.

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