Question

Two wires of the same material have length 6 cm and 10 cm and radii 0.5 mm and 1.5 mm respectively. They are connected in series across a battery of 16 V. the p.d. across the shorter wire is

Answer 1

Answer:

L1 = 6cm = 60mm

L2 = 10cm = 100mm

r1 = 0.5mm

r2 = 1.5mm

Material is same so resistivity would also be same.

A1R1/L1 = A2R2/L2

A1 = pi × 0.5 × 0.5 = 0.25pi

A2 = 2.25pi

R1/R2 = A2L1 / A1L2

R1/R2 = 2.25pi × 60 / 0.25pi × 100

R1/R2 = 225 × 60 / 25 × 100

R1/R2 = 5.4 = 54/10 = 27/ 5

Hence R1 = 27 and R2 = 5

In series total resistance is given by R1 +R2

27 + 5 = 32

i = V/R

i = 16 / 32 = 1/2 = 0.5A

Now p.d across 6 cm wire is

V = iR

V = 0.5 × 27

V = 13.5V

THANKS

Explanation: