The alternating current is given by, i = { 42 sin ( T 2 π t ) + 10 } A . The R.M.S. value of this current is __________ A .

The given function of current is, i = { 42 sin ( T 2 π t ) + 10 } A It means, i 2 = 42 sin 2 ( T 2 π t ) + 100 + 20 42 sin ( T 2 π t ) ⇒ ⟨ i 2 ⟩ = 2 42 + 100 RMS value of the current is, i r m s = ⟨ i 2 ⟩ = 121 = 11 A

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PhysicsEMI/ACAC current and voltageMedium2 minQB

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The alternating current is given by, $i = {42 sin (\frac{2 π}{T} t) + 10} A$ . The R.M.S. value of this current is __________ $A$ .

Answer:

11.00

Solution:

The given function of current is, $i = {42 sin (\frac{2 π}{T} t) + 10} A$

It means, $i^{2} = 42 sin^{2} (\frac{2 π t}{T}) + 100 + 2042 sin (\frac{2 π t}{T})$

$\Rightarrow ⟨ i^{2} ⟩ = \frac{42}{2} + 100$

RMS value of the current is, $i_{r m s} = ⟨ i^{2} ⟩ = 121 = 11 A$

Stream:JEESubject:PhysicsTopic:EMI/ACSubtopic:AC current and voltage

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