Q- A wire of resistance R is cut into n equal parts. These parts are then
connected in parallel. The equivalent resistance of combination will be
(A) nR (B) R/n (C) n/R (D) R/n2
Q- A piece of wire of resistance 4W is bent through 1800 at its mid- point and
the two halves are twisted together, then resistance is :
(A) 1W (B) 2W (C) 5W (D) 8W
Answers
Answer 1:
As we know R∝l(length of wire)
and we are cutting the wire into n equal parts, so each new formed wire's resistor
⇒R
1
=R
2
=R
3
=R
4
=R
5
=...R
n
=
n
R
as the diagram shows, we are connecting them in parallel series then equivalent resistance of combination is given by R
eq
⇒
R
eq
1
=
R
1
1
+
R
2
1
+
R
3
1
+
R
4
1
+...+
R
n
1
⇒
R
eq
1
=
R
n
+
R
n
+
R
n
+...+
R
n
(n times)
⇒
R
eq
1
=(
R
n
)×n
⇒R
eq
=
n
2
R
correct option will be (D)
Answer 2:
A piece of wire with a resistance of 4 ohms is bent at its midpoint and the two halves are twisted together. What is the new resistance?
Total resistance of the full length of the wire= 4 ohms
Resistance of the two pieces of equal length bent at the mid point and free ends brought together= 2 ohms.
When you twiste the wire the resistances of 2 ohms each are connected in parallel together, the effective resistance of the two wire connected in parallel:
1/R = 1/2 + 1/2 =2/2= 1 , therefore effective resistance= 1 ohm.