Question

two wires of same material have same length but their cross sectional area in the ratio 3 is to 1 they are joined in series connection resistance of the thicker wire is 10 ohm find total resistance of the combination

Answer 1

Answer:

Explanation:

resistance of thicker wire = 10 Π

as cross section is inversely proportional to resistance

resistance of smaller wire be r and bigger be R

R=¶l/3a

r=¶l/a

so resistance of bigger wire = r/3

R=r/3

R=10Π

r=10*3=30Π

total resistance =30Π+10Π=40Π

answer =40Π

Answer 2

The total resistance of the combination is 40 ohms.

Explanation:

Let the resistance of thicker wire is R and that of thinner wire is r. Similarly, the area of thicker and thinner wires is A and a respectively. Two wires of same material have same length but their cross sectional area in the ratio 3 is to 1 i.e

$\dfrac{A}{a}=\dfrac{3}{1}$

Resistance of thicker wire is :

$R=\rho\dfrac{l}{A}$ ......(1)

Resistance of thinner wire is :

$r=\rho\dfrac{l}{a}$ ......(2)

Dividing equation (1) and (2) we get :

$\dfrac{R}{r}=\dfrac{\dfrac{\rho l}{A}}{\dfrac{\rho l}{a}}\\\\\dfrac{R}{r}=\dfrac{a}{A}$

$\dfrac{R}{r}=\dfrac{1}{3}\\\\r=3R\\\\r=3\times 10 = 30 \ \Omega$

Equivalent resistance when 30 ohms and 10 ohms are connected in series is : 30 +10 = 40 ohms.

Learn more,

Resistance

https://brainly.in/question/2884619