Question

A wire of resistance 20 Ω is bent to form a closed square. What is the resistance across a diagonal of the square?

Answer 1

ans.
5 ohm
it's correct answer

Answer 2

Answer: 5 Ω

Explanation:

In series, equivalent resistance is given by:

R = R₁+R₂+R₃+....

In Parallel, net resistance is given by:

R = ( R₁×R₂×R₃×..)÷(R₁+R₂+R₃+..)

We can think about the wire as connection of 4 pieces having equal resistance(R) and connected in series.

Thus net resistance = 20 Ω = 4 R

⇒R = 5 Ω

Now the wires make a square and we need to find the resistance across the diagonal. Then, two wires are connected in parallel with two other wires.

Resistance of wires connected in series = 2 R = 2 × 5 Ω = 10 Ω

Now, 10 Ω wires connected in parallel with another 10 Ω wire, the net resistance is :

R = (10Ω×10Ω)÷(10Ω+10Ω) = 5Ω