What is the value of series resistance required to extend the 0 - 100 Volts range of a 20,000 Ω/V meter to 0 - 1000 volts?
18 M Ω
Series Resistance for Voltmeter Range Extension
Extending the range of a voltmeter involves adding a series resistance, often called a multiplier resistance, to the meter. This resistance limits the current flowing through the meter's internal mechanism, allowing it to measure higher voltages without damage. The key principle here is the meter's sensitivity, which remains constant.
Meter Resistance Calculation
First, we need to determine the internal resistance of the voltmeter. A meter's sensitivity (S) is given in Ohms per Volt (\(\Omega\)/V), which represents the total resistance required per volt of full-scale deflection. The meter's internal resistance (\(R_m\)) can be calculated using its sensitivity and its original full-scale voltage range (\(V_1\)).
- Given meter sensitivity, \(S = 20,000 \, \Omega/V\)
- Original voltmeter range, \(V_1 = 100 \, V\)
The meter resistance (\(R_m\)) is calculated as:
\[ R_m = S \times V_1 \] \[ R_m = 20,000 \, \frac{\Omega}{V} \times 100 \, V \] \[ R_m = 2,000,000 \, \Omega \] \[ R_m = 2 \, M\Omega \]Required Total Resistance for Extended Range
Next, we calculate the total resistance required for the desired extended range. The meter sensitivity applies to the entire circuit, including the meter's internal resistance and any external series resistance. The extended range (\(V_2\)) is the new maximum voltage the meter should measure.
- Extended voltmeter range, \(V_2 = 1000 \, V\)
The total resistance (\(R_t\)) needed for the extended range is:
\[ R_t = S \times V_2 \] \[ R_t = 20,000 \, \frac{\Omega}{V} \times 1000 \, V \] \[ R_t = 20,000,000 \, \Omega \] \[ R_t = 20 \, M\Omega \]Series Resistance Determination
The series resistance (\(R_{se}\)) is the additional resistance that needs to be connected in series with the meter's internal resistance to achieve the new, higher voltage range. It is the difference between the total resistance required for the extended range and the meter's original internal resistance.
\[ R_{se} = R_t - R_m \]Substituting the calculated values:
\[ R_{se} = 20 \, M\Omega - 2 \, M\Omega \] \[ R_{se} = 18 \, M\Omega \]Alternatively, the series resistance can also be directly calculated as:
\[ R_{se} = S \times (V_2 - V_1) \] \[ R_{se} = 20,000 \, \frac{\Omega}{V} \times (1000 \, V - 100 \, V) \] \[ R_{se} = 20,000 \, \frac{\Omega}{V} \times 900 \, V \] \[ R_{se} = 18,000,000 \, \Omega \] \[ R_{se} = 18 \, M\Omega \]Therefore, a series resistance of 18 M\(\Omega\) is required to extend the 0 - 100 Volts range of the 20,000 \(\Omega\)/V meter to 0 - 1000 Volts.
Important Questions from Extension Ranges of Basic Meters
The range of a moving iron ammeter can be extended by using a ___________.
Which of the following material is used as a series for range extension of Voltmeter?
An instrument with an internal resistance of 100 Ω and a full-scale current of 1 mA is to be converted into a DC voltmeter with range of 0 V - 500 V. Find the value of the resistance used as a multiplier.
Considering extending the range of measuring instruments, the ratio \(\rm \frac{resistance \ of \ ammeter \ shunt }{resistance \ of \ voltmeter \ multiplier}=?\)
Which of the following can be used to extend the range of ammeter?
