A d.c. circuit can be represented by a voltage source of 10 V in series with an output resistance of 1 k ohm. An ammeter of 50 ohm resistance is connected to the source terminals for measurement of current. what will be the accuracy of measurement?
I=V/(Ro+Ra) = 10/(1k+0.05k) = 9.5238 mA.
= Measured current.
I=10/1k = 10.00 mA=Theoretical current.
Accuracy = ((10.00 - 9.5238)/10)*100%4.762 %.
To determine the accuracy of the current measurement in the given circuit, we need to consider the effect of the ammeter's resistance on the circuit.
Given:
Voltage source = 10 V
Output Resistance = 1 kΩ
Ammeter Resistance = 50 Ω
To calculate the accuracy, we will use the concept of percent error.
Step 1: Calculate the total resistance in the circuit.
The total resistance (R_total) is the sum of the output resistance (R_output) and the ammeter resistance (R_ammeter).
R_total = R_output + R_ammeter
= 1 kΩ + 50 Ω
= 1050 Ω
Step 2: Calculate the current (I) flowing through the circuit using Ohm's law.
Ohm's law states that I = V / R, where V is voltage and R is resistance.
I = V / R_total
= 10 V / 1050 Ω
≈ 0.00952 A
Step 3: Calculate the expected resistance (R_total_expected) if the ammeter had zero resistance.
To determine the expected resistance, we calculate the current using the total voltage and only the output resistance.
R_total_expected = V / I
= 10 V / (10 V / 1 kΩ)
= 1 kΩ
Step 4: Calculate the percent error using the expected resistance and the current measured with the ammeter.
Percent Error = |(R_total - R_total_expected) / R_total_expected| * 100
Substituting the values:
Percent Error = |(1050 Ω - 1000 Ω) / 1000 Ω| * 100
= |50 Ω / 1000 Ω| * 100
= 5%
Therefore, the accuracy of the current measurement using the ammeter in this circuit is 5%.
To determine the accuracy of the current measurement, we need to consider the impact of the internal resistance of the ammeter on the circuit.
In this case, the ammeter has a resistance of 50 ohms (as given in the question). Since it is connected in series with the circuit, it will affect the overall resistance in the circuit.
To calculate the total resistance, we need to add the output resistance of the circuit (1 kΩ) and the resistance of the ammeter (50 Ω):
Total resistance = Output resistance + Ammeter resistance
Total resistance = 1 kΩ + 50 Ω = 1050 Ω
We can now calculate the current flowing through the circuit using Ohm's law:
Current (I) = Voltage (V) / Total resistance
Current (I) = 10 V / 1050 Ω
Now, let's calculate the accuracy of the measurement. The accuracy is typically expressed as a percentage of the full-scale reading. In this case, the full-scale reading is the maximum possible current flowing through the circuit.
To find the maximum current, we consider the scenario when the circuit's output resistance is negligible compared to the ammeter resistance. It means that all the voltage provided by the source would be across the internal resistance of the ammeter.
Maximum current (Imax) = Voltage (V) / Ammeter resistance
Maximum current (Imax) = 10 V / 50 Ω
Maximum current (Imax) = 0.2 A
Now, let's calculate the accuracy:
Accuracy = (Measured current / Maximum current) * 100%
Accuracy = (I / Imax) * 100%
Accuracy = (10 V / 1050 Ω) / (0.2 A) * 100%
After substituting the values, we can calculate the accuracy. However, note that the unit of the resistance is changing to kilohms (kΩ) in the denominator:
Accuracy = (0.009524 A / 0.2 A) * 100%
Accuracy ≈ 4.76%
Therefore, the accuracy of the current measurement in this circuit is approximately 4.76%.