Show that Volt-Ampere is equal to Watt (SI unit of power).

To show that Volt-Ampere (VA) is equal to Watt (W), let’s analyze the units step by step.

Step 1: Define Power

Electrical power ($P$) is given by:

P=V×I

where:

• V is the voltage in volts (V),
• $I$ is the current in amperes (A).

Step 2: Express SI Units

The SI unit of voltage (V) is:

1 V=1Joule/Coulomb=1kg⋅m²/s³⋅A​

The SI unit of current ($A$) is:

1 A=1 Coulomb per second

=1C/s​

Multiplying these:

1 V×1 A=(1kg⋅m²/s³⋅A)×(1 A)

Since amperes cancel out, we get:

1kg⋅m²/s³=1 Watt (W)

Conclusion:

Since 1 Volt × 1 Ampere = 1 Watt, the unit Volt-Ampere (VA) is dimensionally equal to the Watt (W), the SI unit of power.