A resistance in a circuit is 470§Ù ¡¾ 10%. When a meter with a full-scale voltage of 25V and error of ¡¾ 3% is used to measure the voltage across the resistance, the voltage was read as 12V. Obtain the power across the resistance and determine its error.
To obtain the power across the resistance, we need to use the formula:
Power (P) = (V^2) / R
where V is the voltage across the resistance and R is the resistance.
Given:
Resistance (R) = 470Ω ± 10%
Voltage (V) = 12V
Full-scale voltage of the meter (V_full-scale) = 25V
Error of the meter (Error_meter) = ±3%
Step 1: Calculate the actual resistance value
To determine the actual resistance value, we need to calculate the minimum and maximum resistance values based on the given tolerance of ±10%.
Minimum resistance (R_min) = R - (R * 10%)
= 470Ω - (470Ω * 0.10)
= 470Ω - 47Ω
= 423Ω
Maximum resistance (R_max) = R + (R * 10%)
= 470Ω + (470Ω * 0.10)
= 470Ω + 47Ω
= 517Ω
The actual resistance lies between 423Ω and 517Ω.
Step 2: Calculate the actual power value
To determine the actual power value, we substitute the voltage and the actual resistance into the power formula.
Actual Power (P_actual) = (V^2) / R_actual
P_actual_min = (12V^2) / 517Ω
= 144V^2 / 517Ω
= 0.2787 W (rounded to 4 decimal places)
P_actual_max = (12V^2) / 423Ω
= 144V^2 / 423Ω
= 0.3403 W (rounded to 4 decimal places)
The actual power lies between 0.2787W and 0.3403W.
Step 3: Calculate the error in power
The power error can be calculated as the difference between the maximum and minimum power values divided by two.
Power Error (Error_power) = (P_actual_max - P_actual_min) / 2
Error_power = (0.3403W - 0.2787W) / 2
= 0.0308 W (rounded to 4 decimal places)
Therefore, the power across the resistance is approximately 0.3095W, with an error of ±0.0308W.