Question

An electric lamp of 100 Ω, a toaster of resistance 50 Ω and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to same source that takes as much current as all three appliances and what is the current through it?​

Answer 1

${\huge {\bf {\underbrace {Question}}}}$

An electric lamp of 100 Ω, a toaster of resistance 50 Ω and a water filter of resistance 500 Ω are connected in parallel to a 220 V source. What is the resistance of an electric iron connected to same source that takes as much current as all three appliances and what is the current through it?

${\huge {\bf {\underbrace {Answer}}}}$

Given,

Resistance of the electric lamp ${\sf {{R}_{1}}}$ = 100 Ω

Resistance of toaster, ${\sf {{R}_{2}}}$ = 50Ω

Resistance of water filter, ${\sf {{R}_{3}}}$= 500 Ω

Since the three appliances are connected in parallel therefore their equivalent resistance is

${\large {\boxed {\pink {\sf {\frac{1}{{R} _ {p}} = \frac{1}{{R} _ {1}} + \frac{1}{{R} _ {2}} + \frac{1}{{R} _ {3}}}}}}}$

${\large {\sf {\implies {\frac{1}{{R}_{p}} = \frac{1}{100} + \frac{1}{50} + \frac{1}{500}}}}}$

${\large {\sf {\implies {\frac{1}{{R}_{p}} = \frac{5+10+1}{500}}}}}$

${\large {\sf {\implies {\frac{1}{{R}_{p}} = \frac{16}{500}}}}}$

${\green {\boxed {\sf {\implies {{R}_{p} = \frac{125}{4}Ω}}}}}$

Now,

$\dagger\bold{current\:through\:the\:three\:appliances\:is}$

${\boxed {\sf {\pink {I = {\frac{V}{R}}}}}}$

${\large {\sf {\implies {I = 220 \times {\frac{4}{125}}}}}}$

${\green {\boxed {\sf {\implies {I = 7.04\: A}}}}}$

Since, the electric iron is connected to the same source (i.e., 220 V) and takes as much current as all three appliances i.e., I = 7.04 A, therefore its resistance is equal to

${\large {\pink {\boxed {\sf {R = {\frac{V}{I}}}}}}}$

${\large {\sf {\implies {R = {\frac{220}{7.04}}}}}}$

${\sf {\green {\boxed {\implies {R = 31.25 Ω}}}}}$

Current through the electric iron, I = 7.04 A.

Answer 2

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