Question
Two resistances are given as R_1=(10 0.5) and R_2=(15 0.5) . The percentage error in the measurement of equivalent resistance when they are connected in parallel is
BITSAT
Physics
Mathematics in Physics
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Physics Question (2023) — Solution
Options
- A. 6.33
- B. 2.33
- C. 4.33
- D. 5.33
Answer
C. 4.33
Step-by-step solution
Equivalent resistance in parallel combination is given by aligned & 1 R_ eq = 1 R_1 + 1 R_2 \\ & R_ eq = R_1 R_2 R_1+R_2 = 10 15 10+15 =6 aligned Differentiating both sides, we get aligned & R_ eq R _ eq ^2 = R _1 R _1^2 + R _2 R _2^2 \\ & R _ eq R _ eq = ( R _1 R _1^2 + R _2 R _2^2 ) R _ eq \\ & = ( 0.5 100 + 0.5 225 ) 6= ( 6 0.5 25 ) ( 1 4 + 1 9 )= 13 300 \\ & R _ eq R _ eq 100= 13 3 =4.33 \% aligned
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