Question

Two lamps, one rated 100 W; 220V, and the other 60W; 220V, are connected in parallel to the electric mains supply. Find the current drawn by two bulbs from the line, if the supply voltage is 220V.
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Answer 1

$\underline\blue{\bold{ANSWER}}$:-

first lamp rated 100W , 220v (Given)

$R_{1} = \large \frac{ {220}^{2} }{100}$

second lamp 60 W , 220v

$\large\ R_{2} = \frac{ {220}^{2} }{60}$(According to joule's law of heating - $\large\ p = \large\frac{ {V}^{2} }{R} )$

$\blue{\texttt{They\: are \: connected\: in\: parallel\: to\: the}}$

$\blue{\texttt{electric\: main \: supply\: so\: then,}}$

$\large\frac{1}{ R_{eq} } = \large\frac{1}{ R_{1}} + \large \frac{1}{ R_{2} }$

= $\large\frac{1}{ {220}^{2} /100 } + \large \frac{1}{ {220}^{2} / 60 }$

$R _{eq} = \large\ {220}^{2} /160$

from ohm's law,

$V = IR_{eq}$

$200 = \large\frac{ {220}^{2} }{160} I$

$\underline\blue{\bold{I = 0.73A}}$.

SO , $\underline\red{\bold{the \: current \: drawn \: by \: two \: bulbs \: from}}$

$\underline\red{\bold{the \: line \: is \:0.73A}}$

Answer 2

Given that -

✠ There are two lamps that are connected in parallel to the electric main supply.

✠ One of the lamp rated as 100 W ; 220 V

Means,

R₁ = 220² / 100

✠ The another lamp rated 60 W ; 220 V

Means,

R₂ = 220²/60

To find -

✠ Current

Solution -

✠ Total current = 0.73 A

Using concept -

✰ Resistance (parallel connection).

✰ Ohm's law

Using formula -

✰ Resistance (parallel connection) = 1/R = 1/R₁ + 1/R₂ .... 1/Rn

✰ Ohm's law => V = IR

Where,

★ I denotes total current

★ R denotes resistance

Final solution -

~ Now,

➝ 1/R = 1/R₁ + 1/R₂ .... 1/Rn

➝ (1/220² / 100) + (1/220² / 60)

• Cancelling the digits,

➝ R = 220² / 60

~ Using ohm's law

➝ V = IR

➝ V = 220²/106 I

➝ V = 48400/160 I

➝ 200 = 48400/160 I

➝ 200 = 4840/16 I

• Cancelling the digits

➝ 200 = 605/2 I

➝ 200 = 302.5 I

➝ 200 / 302.5 = I

➝ 0.73 = I

➝ I = 0.73 A

Additional information -

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Kinetic \: energy \: is \: given \: by \: \dfrac{1}{2}mv^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Value \: of \: G \: is \: 6.673 \times 10^{-11}Nm^{2}kg^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Dimensional \: formula \: for \: universal \: gravitational \: constant \: is \: M^{-1} L^{3} T^{-2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto The \: unit \: of \: force \: constant \: k \: of \: a \: spring \: is \: \dfrac{N}{m}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Sir \: Cavendish \: was \: the \: first \: to \: gave \: value \: of \: G \: experimentally}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto The \: Young's \: modulus \: for \: perfect \: rigid \: body \: is \: infinite}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Density \: is \: the \: ratio \: of \: \dfrac{Volume}{Mass}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Maxwell \: is \: unit \: of \: magnetic \: flux}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: magnetic \: flux \: is \: Weber}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: surface \: tension \: is \: \dfrac{N}{m}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: mechanical \: power \: is \: Watt}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto 1 \: horsepower \: = \: approx \: 746 \: watts}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Momentum \: is \: measured \: as \: the \: product \: of \: Mass \: and \: velocity}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto \pi \: 'pi' \: is \: calculated \: by \: Aryabhatta}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto One \: J \: = \: 0.24 \: cal}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Number \: of \: SI \: units \: are \: 7}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Ampere \: is \: the \: unit \: of \: current \: electricity}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: Young's \: modulus \: of \: elasticity \: is \: Newton/m^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: pressure \: is \: Pascal}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Curie \: is \: the \: unit \: of \: radio \: activity}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Decibel \: is \: the \: unit \: of \: intensity \: of \: sound}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: electric \: charge \: is \: coulomb}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: resistance \: is \: ohm}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SI \: unit \: of \: acceleration \: is \: ms^{-2}}}}$