Question

Derive the power in terms of voltage and current.​

Answer 1

Explanation:

The formula of power is

$\boxed{\sf Power=Volt \times Current}$

$\sf \leadsto p = vi$

$\sf \leadsto 1watt=1volt\times 1Ampere$

$\sf \leadsto 1w=1v\times 1A$

Answer 2

Short form Used:-

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• P = Power
• W = Work done
• T = Time
• V = Voltage
• Q = Quantity of charge
• I = Current

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Derivation:-

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Power is defined as Rate of doing work.

Hence,

${\boxed{\tt{Power = \frac{WorkDone}{Time}}}}$

$\tt{P =\frac{W}{T}------eq.1}$

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We know that the work done by electrical energy is equals to the potential difference times quality of charge flowing through the conductor.

$\tt{\therefore W = VQ ------eq.2}$

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Putting the value of eq.2 in eq.1

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$\tt{\therefore P = \frac{VQ}{T} ------eq.3}$

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We know that the quantity of charge flowing through a conductor per unit is called current.

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$\tt{\therefore I = \frac{Q}{T}}$

$\tt{ ➟ Q = IT ------eq.4}$

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Putting eq.4 in eq.3

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$\tt{\therefore P = \frac{VI\cancel{T}}{\cancel{T}}}$

$\tt{\therefore P = VI }$

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Hence,

Power = Voltage × Current.

Derived✔