Two resistance are given as R1=(10±0.5) Ω and R2=(15±0.5) Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is
Question
Two resistance are given as R1=(10±0.5) Ω and R2=(15±0.5) Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is
Solution
The equivalent resistance (R) when two resistors are connected in parallel is given by the formula:
1/R = 1/R1 + 1/R2
First, calculate the equivalent resistance using the given values of R1 and R2:
1/R = 1/10 + 1/15 1/R = 0.1 + 0.0667 1/R = 0.1667 R = 6 Ω
Next, calculate the percentage error in the measurement of each resistor. The percentage error is given by the formula:
Percentage error = (Absolute error / Measured value) * 100%
For R1: Percentage error = (0.5 / 10) * 100% = 5%
For R2: Percentage error = (0.5 / 15) * 100% = 3.33%
When resistors are connected in parallel, the percentage errors are added together:
Total percentage error = Percentage error of R1 + Percentage error of R2 Total percentage error = 5% + 3.33% = 8.33%
So, the percentage error in the measurement of the equivalent resistance when the resistors are connected in parallel is 8.33%.
Similar Questions
Determination of the Equivalent Resistance of Two Resistors When Connected in Parallel
If two resistors with resistances R1 and R2 are connected in parallel, as in the figure below, then the total resistance R, measured in ohms (Ω), is given by 1R = 1R1 + 1R2.If R1 and R2 are increasing at rates of 0.3 Ω/s and 0.2 Ω/s, respectively, how fast is R changing when R1 = 90 Ω and R2 = 110 Ω? (Round your answer to three decimal places.)
A 100-Rresistor and another resistor in parallel have an equivalent resistance of 75 R. What is the resistanceof the other resistor?
The effective resistance is Ω, when two wires are joined in parallel. When one of the wire breaks, the effective resistance is 2 ohms. The resistance of the broken wire was :
A piece of wire of resistance R is cut into five equal parts. These parts are thenconnected in parallel. If the equivalent resistance of this combination is R′, then theratio R/R′ is –
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.