Question

A 100ohm resistor is connected to a 220v, 50Hz supply. (i)What is rms value of current in the circuit (ii) what is net power consumed over a full cycle?

Answer 1

(i)

$i(rms) = \frac{i}{ \sqrt{2} }$

$i = \frac{220}{100} = 2.2 \: ampere$

$i(rms) = \frac{2.2}{ \sqrt{2} }$

$i(rms) = 1.55 \: ampere$

(ii) In a purely resistive circuit, the phase difference between current and voltage is 0

Since,

$p = i(rms) \times v(rms) \times \cos( \alpha )$

So,

$p = i(rms) \times v(rms) \times 1$

$p = \frac{i}{ \sqrt{2} } \times \frac{v}{ \sqrt{2} }$

$p = 2.2 \times 220$

$p = 484 \: watt$

Answer 2

$\huge\rm\underline\purple{Question :-}$

A 100Ω resistor is connected to a 220ν , 50ΗΖ ac supply.

a. what is the rms value of current in the circuit ?

b. what is the net power consumed over a full cycle?

$\huge\rm\underline\red{Answer :-}$

$\green{\underline\bold{Given,}}$

• R = 100 Ω
• V = 220 Vrms
• f = 50 Hz
• ω = 2Πf = 2 × 3.14 × 50 = 314

a.) Using the Relation,

$\boxed{ \sf \pink{ Irms \:=\frac{Vrms}{R} }}$

$\blue{\underline\bold{Now,}}$

Putting the values,

$\orange{\underline\bold{Irms\:=\frac{220}{100}}}$

= 2.2 A

$\purple{\underline\bold{∴\:The \:rms\: value\: of \:current \:in\: the\: circuit=\:2.2A}}$

a.) We Know,

$\boxed{ \sf \blue{ Power\: consumed,P\:= \frac{V\:^2}{R} }}$

= $\frac{220\:^2}{100}$

= 484 watt.

$\purple{\underline\bold{∴\:The \:Net\:power\: consumed\:over \:a\: full\: cycle=\:484\:watt.}}$

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