Question

An alternating EMF e= 40 sin( 120 πt) in volt is connected across a 100 ohm resistor calculator The RMS current through the resistor​

Answer 1

Answer:

Hope it will help you.Use the rules properly

Answer 2

The RMS Current through the resistor is equal to 0.28 Ampere.

Given:

The alternating EMF: e = 40sin (120πt)

The resistance of the resistor = 100 Ω

To Find:

The RMS current through the resistor.

Solution:

$\boldsymbol{The\:relation\:between\:the\:Peak\:Voltage\:(V_{0})\:and\:the\:R.M.S.\:Voltage\:(V_{RMS})\: is: }$

                  $\fbox{\boldsymbol{RMS\:Voltage\:(V_{RMS})=\frac{Peak\:Voltage\:(V_{0})}{\sqrt{2} } \: }}$            

  $\boldsymbol{The\:relation\:between\:the\:Peak\:Current\:(i_{0})\:and\:the\:R.M.S.\:Current\:(i_{RMS})\: is: }$

                  $\fbox{\boldsymbol{RMS\:Current\:(i_{RMS})=\frac{Peak\:Current\:(i_{0})}{\sqrt{2} } \: }}$

In the given question:

The alternating EMF: e = 40sin (120πt)

∴ The Peak Voltage (V₀) = 40 V

∵ The resistance (R) of the resistor = 100 Ω

∴ The Peak Current (i₀) = (40)/100 = 0.4 Ampere

                 $\fbox{\boldsymbol{\because RMS\:Current\:(i_{RMS})=\frac{Peak\:Current\:(i_{0})}{\sqrt{2} } \: }}\\\\\boldsymbol{\therefore RMS\:Current\:(i_{RMS})=\frac{0.4}{\sqrt{2} }=0.28\:Ampere }$

The value of the RMS current comes out to be equal to 0.28 Ampere.                  

             

Therefore the RMS Current through the resistor is equal to 0.28 Ampere.

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