a piece of wire of resistance R is cut into 3 equal parts. These parts are then connected in parallel if the equivalent resistance of the parallel combination is R1 what is the value of ratio R1:R?
Share
a piece of wire of resistance R is cut into 3 equal parts. These parts are then connected in parallel if the equivalent resistance of the parallel combination is R1 what is the value of ratio R1:R?
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Explanation:
tep 1: Resistance of each part after cutting
We know that, Resistance
R
=
ρ
ℓ
A
Since,
R
is directly proportional to length of the wire.
Therefore the resistance of every part after cutting the wire in
5
parts is
R
1
=
R
2
=
R
3
=
R
4
=
R
5
=
R
5
Step 2: Equivalent Resistance
When all the resistances are connected in parallel, let R' be the equivalent resistance
So,
1
R
′
=
1
R
1
+
1
R
2
+
1
R
3
+
1
R
4
+
1
R
5
⇒
1
R
′
=
5
R
+
5
R
+
5
R
+
5
R
+
5
R
⇒
R
′
=
R
25
⇒
R
R
′
=
25