CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Potential Energy - External Viewpoint

Two wires of ...

Question

Two wires of the same material have lengths 3 cm and 5 cm and radii 1 mm and 3 mm respectively. They are connected in series across a battery of 16 V. The p.d. across the shorter wire is

A

2.5 V

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

6.5 V

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

1.5 V

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

13.5 V

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $13.5 V$
Length $= 3 c m$ $(L_{1}) = 60 m m$
$5 c m (L_{2}) = 100 m m$
radii $= 1 m m (r_{1}) = 0.5 m m$
$= 3 m (r_{2}) = 1.5 m m$
The $E M F$ of the battery $= 16 V$
material is same so resistivity would also be same
$\frac{A i r 1}{L_{1}} = A$
$\frac{A_{1} R_{1}}{L_{1}} = \frac{A_{2} R_{2}}{L_{2}}$
$A_{1} = π (0.5) \times 0.5 = 0.25 P i$
$\frac{R_{1}}{R_{2}} = \frac{A_{2} L_{1}}{A_{1} L_{2}}$
$\frac{R_{1}}{R_{2}} = \frac{2.25 π \times 60}{0.25 π \times 100}$
or, $\frac{R_{1}}{R_{2}} = \frac{225 \times 60}{25 \times 100}$
or $\frac{R_{1}}{R_{2}} = 5.4 = \frac{54}{10} = \frac{27}{5}$
(Hence, $R_{1} = 27$ and $R_{2} = 5$ )
Since they are in series $R_{1} + R_{2} = 27 + 5 = 32$
$i = \frac{V}{R}$
$i = \frac{16}{32} = \frac{1}{2} = 0.5 A$
Now, $P d$ across $6 c m$ wire is
$V = i R$
$= 0.5 \times 27$
$= 13.5 V$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Two wires of the same material and having lengths in the ratio of 2:3 are connected in series. The p.d.s across the wires are 4.2 V and 3.6 V respectively. Compare their radii.

A

B

made of same material and having their lengths in the ratio

6 : 1

are connected in series. The potential difference across the wire are

3 V

2 V

respectively. If

r_{A}

r_{B}

are the radii of

A

B

respectively, then

\frac{r_{B}}{r_{A}}

Q. Two wires of the same material having lengths in the ratio 2:3, are connected in series. The potential differences across the wires are 4.2V and 3.6V respectively. The ratio of their radii would be:

Q. Two nichrome wires

A

B

, each of length

5 c m

1 c m

3 c m

respectively are connected to each other in series. If a current of

5 A

flows through the combination of wires, the ratio of potential difference across wire

A

to that across wire

B

Q. Two metallic wire of same material and same length have different diameters when connected in series across a battery, the heat produced in thinner wire is

Q_{1}

and that in thicker one is

Q_{2}

. the correct relation is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Potential Energy of a System of Point Charges

PHYSICS

Watch in App

explore_more_icon

Explore more

Potential Energy - External Viewpoint

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon