Two resistors of resistances R = 10 ± 0.3 ohm and R = 20 ± 0.4 ohm are connected in parallel. The
equivalent resistance of the parallel combination in ohm is
Answers
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
Two resistors of resistances R
1
= (100 ± 3) Ω and R
2
= (200 ± 4) Ω are connected in parallel. The equivalent resistance of the parallel combination is:
Medium
Correct option is A)
Step 1: Calculation of equivalent resistance
R
eq
1
=
R
1
1
+
R
2
1
=
100
1
+
200
1
⇒R
eq
=
3
200
=66.7Ω
Step 2: Error in equivalent resistance
R
eq
1
=
R
1
1
+
R
2
1
⇒R
eq
−1
=R
1
−1
+R
2
−1
Differentiating on both the sides:
R
eq
2
−dR
=
R
1
2
−dR
1
+
R
2
2
−dR
2
OR
R
eq
2
ΔR
=
R
1
2
ΔR
1
+
R
2
2
ΔR
2
Step 3: Calculations
ΔR=R
eq
2
(
R
1
2
ΔR
1
+
R
2
2
ΔR
2
)
Substituting all the values:
ΔR
eq
=(
3
200
)
2
(
(100)
2
3
+
(200)
2
4
)
=(
9
4
)(
1
3
+
4
4
) =
9
16
ΔR
eq
=1.8Ω
Therefore,
R
eq
=66.7±1.8Ω