Year 12s: what will be the first way you research your future options? >>

Hard electrical circuits question, please help

A short circuit has occurred somewhere along a telephone cable that is 10 km long. To determine the location of the short, an engineer measures the resistance between the terminals at both ends. She measures 25 Ω at the start and 80 Ω at the end. Where is the short circuit?

Reply 1

siamsam

2380 metres from the terminal which measures 25 ohms perhaps

(edited 5 years ago)

Reply 2

lmrice

Original post by siamsam

2380 metres from the terminal which measures 25 ohms perhaps

That matches the answer! Would you please be able to show how you achieved that step by step? it would help a bunch. thank you

Reply 3

siamsam

Draw it out on paper first.
You have two wires which have a short circuit somewhere along the length.
The total resistance for the two circuits is 80 + 25 = 105 ohms.
The total length of the two wires is 20000 metres so the resistance per metre is 105 ÷ 20000 = 0.00525

You now need to calculate how many metres of wire are there in the length which measures 25 ohms across its terminals

25 ÷ 0.00525 = 4761 metres

This is the length of the wire from one terminal up to the short and back to the other terminal so you need to divide this figure by 2

4761 ÷ 2 = 2380