Two wires of same material having lengths in the ratio 1:2 and diameter in the ratio 2:3 are connected in series to a battery. Calculate the ration of potential differences across the two wires

Open in App

Solution

Dear student,
We know that,
V=IR
and,
R=ρL/A
Since the two wires of the same material are connected in series, the current flowing through them will be same and hence potential difference across the wire will be directly proportional to L/A.
V=IR=IρL/A=IρL/(d/2)²
V∝l /d²
So, the ratio of potential difference will be

$\frac{V 1}{V 1} = \frac{l 1}{l 2} {\frac{(d 2)}{(d 1)^{2}}}^{2} = \frac{1}{2} \frac{(3)^{2}}{(2)^{2}}$ ^{=9/8

Thus, the ratio of potential difference is 9:8.}

Regards

Suggest Corrections

Similar questions

Q. Two wires of the same material having lengths in the ratio of

1 : 2

and diameters in the ratio of

2 : 3

are connected in series with an accumulator. Compute the ratio of the potential difference across the two wires.

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 wires of the same material having lengths in the ratio of 1 : 2 and diameters in the ratio 2 : 1 are connected with a cell of 6 volt and internal resistance

1 Ω

. The ratio of the potential difference across the two wires will be:

1. Two conducting wires of the same material and equal lengths and equal diameters are first connected in series and then in parallel in a circuit across the same potential difference . What is the ratio of heat produce in series and parallel combinations?

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.

Join BYJU'S Learning Program