calculate the resistance Rab when all the resistance values are 1ohm resistance for the circuit
Answers
Answer:
Explanation:
Let R
AB
=x be equivalent resistance of system between A and B. As the resistance of a conductor is directly proportional to length, the equivalent resistance between A1 and B1 will be x/2. Therefore, the equivalent circuit becomes as given in Fig.Effective resistance of 2r and x/2 is
R
1
=
2r+
2
x
2r
2
x
=
4r+x
2rx
Now R
1
is in series with AA
1
and BB
1
; therefore, their effective resistance is R
2
=R
1
+2r=
4r+x
2rx
+2r
R
2
is in parallel with 2r(ofAB), so the net effective resistance across AB is
x=
R
2
+2r
R
2
×2r
=
[
4r+x
2rx
+2r]+2r
[
4r+x
2rx
+2r]2r
or 3x
2
−4rx−8r
2
=0 or x=
2×3
−4r±
16r
2
+4×3×8r
2
As x cannot be negative, we have
x=
6
−4r+
16r
2
+96r
2
=
3
(2
7
−2)
r
But 2r=aλ or r=aλ2, so
x=
3
2(
7
−1)
×
2
a
λ=0.55aλ