Question

plzzz help......??? ​

Answer 1

$\large{\underline{\underline{\red{\sf{\hookrightarrow Given :-}}}}}$

Two wires A and B are of same material.

Their ratio of lenght is 1 : 2 .

Ratio of their cross - Sectional area is 2 : 3.

Resistance of wire A is 12Ω.

$\large{\underline{\underline{\red{\sf{\hookrightarrow To\:Find:- }}}}}$

The resistance of wire B .

$\large{\underline{\underline{\red{\sf{\hookrightarrow Formula\:Used:- }}}}}$

We know that when length and area are given , we can calculate resistance by using formula ,

$\large\pink{\underline{\boxed{\purple{\tt{ \dag \:\: Resistance\:\:=\:\:\rho\:\dfrac{l}{a}}}}}}$

✒️ Where ,

l is lenght.

a is area .

$\rho$ is resistivity or specific resistance.

$\large{\underline{\underline{\red{\sf{ \hookrightarrow Calculation:-}}}}}$

Let us take the ratio of length of two wires be x : 2x .

And , the ratio of their cross - sectional areas be 2y : 3y .

Let us denote ,

❒ $\tt{R_1\:as\: resistance\: of\:wire\:A.}$

❒ $\tt{R_2\:as\: resistance\: of\:wire\:B.}$

Now , Resistance of Wire A :-

$\tt:\implies Resistance =\rho\dfrac{l}{a}$

$\pink{\tt:\longmapsto R_1 = \rho\dfrac{x}{2y} \:\:.............(i)}$

Similarly, Resistance of Wire B :-

$\tt:\implies Resistance =\rho\dfrac{l}{a}$

$\pink{\tt:\longmapsto R_2 = \rho\dfrac{2x}{3y} \:\:.............(ii)}$

Now divide equⁿ (i) and equⁿ (ii) ,

$\tt:\implies \dfrac{R_1}{R_2}=\dfrac{\cancel{\rho}\dfrac{x}{2y}}{\cancel{\rho}\dfrac{2x}{3y}}$

$\tt:\implies \dfrac{R_1}{R_2}=\dfrac{\cancel{x}\:\:\times\:\:3\cancel{y}}{2\cancel{y}\:\:\times\:\:2\cancel{x}}$

$\tt:\implies \dfrac{R_1}{R_2}=\dfrac{1\:\:\times\:\:3}{2\:\:\times\:\:2}$

$\tt:\implies \dfrac{12\Omega}{R_2}=\dfrac{3}{4}$

$\tt:\implies R_2=\dfrac{\cancel{12}^{4}\times4}{\cancel{3}}$

$\underline{\boxed{\red{\tt{\longmapsto\:\:R_2\:\:=\:\:16\Omega}}}}$

$\boxed{\bf{\green{\dag Hence\:the\: resistance\:of\:wire\:B\:is\:16\: \Omega.}}}$

Answer 2

$\huge{\underline{\underline{\boxed{\sf{\purple{Answer ࿐}}}}}}$

750 ml of 0.5 M HCl have 0.375 moles.

250 ml of 2 M HCl have 0.5 moles.

Total moles =0.875moles

Total volume =750+250=1000ml=1L

Molarity =

Volume

Moles

=

1

0.875

=0.875M

Hence, the correct option is D.