Limiting Error of Measurement of Resistance

Given:

- Limiting error of measurement of power consumed = 2%
- Limiting error of measurement of voltage = 3.5%

The formula for power is:

P = V^2/R

where P is power, V is voltage, and R is resistance.

The formula for percentage error is:

%error = (error/reading) x 100

where error is the maximum error and reading is the maximum reading.

Let's calculate the maximum error in power:

%error in power = 2%

This means that the maximum error in power is 2% of the maximum reading.

Let's calculate the maximum error in voltage:

%error in voltage = 3.5%

This means that the maximum error in voltage is 3.5% of the maximum reading.

Let's calculate the maximum error in resistance:

We can rearrange the formula for power to get the formula for resistance:

R = V^2/P

Let's differentiate this formula with respect to V and P:

∂R/∂V = 2V/P^2

∂R/∂P = -V^2/P^2

Let's calculate the percentage error in resistance using the formula for error propagation:

%error in resistance = sqrt((%error in voltage)^2 + 4*(%error in power)^2 + (2*∂R/∂V)^2*(%error in voltage)^2 + (2*∂R/∂P)^2*(%error in power)^2)

%error in resistance = sqrt((3.5%)^2 + 4*(2%)^2 + (2*2V/P^2)^2*(3.5%)^2 + (-V^2/P^2)^2*(2%)^2)

Assuming that the maximum error occurs when V and P are at their maximum values:

%error in resistance = sqrt((3.5%)^2 + 4*(2%)^2 + (2*Vmax/Pmin^2)^2*(3.5%)^2 + (-Vmax^2/Pmax^2)^2*(2%)^2)

Let's assume that the voltage and power are equal, i.e. Vmax = Pmax = V.

%error in resistance = sqrt((3.5%)^2 + 4*(2%)^2 + (2*V/P^2)^2*(3.5%)^2 + (-V^2/P^2)^2*(2%)^2)

%error in resistance = sqrt(0.1225 + 0.16 + (0.035V/P)^2 + (0.04V^4/P^4))

Let's assume that the voltage and resistance are equal, i.e. V = R.

%error in resistance = sqrt(0.1225 + 0.16 + (0.035R/R^2)^2 + (0.04R^4/R^4))

%error in resistance = sqrt(0.1225 + 0.16 + 0.01225 + 0.04)

%error in resistance = sqrt(0.33475)

%error in resistance = 0.5784

%error in resistance = 5.784%

Therefore, the limiting error of measurement of resistance is 9%.