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Two resistors R1 and R2 are connected in series. The voltage across the series combination is V. A voltmeter V1 is used to measure the voltage across the resistor R1 and a voltmeter V2 is used to measure the voltage across the resistor R2.
The voltmeter V1 is ±X% and the voltmeter V2 is +y% accurate. The voltmeter V1 reads 10 V and V2 reads 5 V. The absolute error of two voltmeters are the same and absolute error in total voltage V is 0.2 V.
The values of X and Y (in %) respectively are:
  • a)
    1%, 2%
  • b)
    0.5%, 1%
  • c)
    1%, 0.5%
  • d)
    2%, 1%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two resistors R1 and R2 are connected in series. The voltage across t...
The voltmeter V1 is ±x% and voltmeter V2 is +y% accurate
V1 = 10V, V2 = 5
Absolute error,
∨1 = x100 × 10 = 0.1x
V2 = y100 × 5 = 0.05y
Absolute error of two voltmeter are same
0.1x = 0.05y
y = 2x −(i)
Total voltage, V = V1 + V2
Absolute error in total voltage,
V = 0.1 x + 0.05y
0.2 = 0.1 x + 0.05y
Put equation (i) in above expression
0.2 = 0.1 x + (0.05)2x
⇒x=1%, y=2%
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Most Upvoted Answer
Two resistors R1 and R2 are connected in series. The voltage across t...
Given Data:
- Two resistors R1 and R2 connected in series
- Voltage across the series combination = V
- Voltmeter V1 measures voltage across R1 with ±X% accuracy
- Voltmeter V2 measures voltage across R2 with ±Y% accuracy
- V1 reads 10 V and V2 reads 5 V
- Absolute error in total voltage V = 0.2 V

To Find:
The values of X and Y (in %)

Solution:

Step 1: Calculate the Resistance:
When resistors are connected in series, the total resistance (Rt) is the sum of individual resistances (R1 and R2).
So,
Rt = R1 + R2

Step 2: Calculate the Current:
Using Ohm's Law, we can calculate the current (I) flowing through the circuit.
V = I * Rt
=> I = V / Rt

Step 3: Calculate the Voltage across R1 and R2:
Using Ohm's Law, we can calculate the voltage across R1 and R2.
V1 = I * R1
V2 = I * R2

Step 4: Calculate the Relative Error:
Relative error is given by:
Relative Error = (Measured Value - True Value) / True Value * 100

For V1:
Relative Error in V1 = (Measured V1 - True V1) / True V1 * 100
=> X = (10 - True V1) / True V1 * 100

For V2:
Relative Error in V2 = (Measured V2 - True V2) / True V2 * 100
=> Y = (5 - True V2) / True V2 * 100

Step 5: Calculate True V1 and True V2:
Since the voltmeters have some absolute error, we can calculate the true values of V1 and V2 by subtracting the absolute error.
True V1 = Measured V1 - Absolute Error
True V2 = Measured V2 - Absolute Error

Step 6: Calculate True Rt:
From Step 3, we know that V1 = I * R1 and V2 = I * R2.
Substituting the values of V1 and V2 from Step 5:
True Rt = True V1 / I + True V2 / I
=> True Rt = (Measured V1 - Absolute Error) / I + (Measured V2 - Absolute Error) / I

Step 7: Calculate True V:
Using Ohm's Law: V = I * True Rt
=> True V = I * True Rt

Step 8: Calculate X and Y:
From Step 4, we have the relative errors in V1 and V2.
Substituting the values of True V1 and True V2 from Step 5:
X = (10 - (Measured V1 - Absolute Error)) / (Measured V1 - Absolute Error) * 100
Y = (5 - (Measured V2 - Absolute Error)) / (Measured V2 - Absolute Error) * 100

Step 9: Calculate the Values:
Substituting the given
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Two resistors R1 and R2 are connected in series. The voltage across the series combination is V. A voltmeter V1 is used to measure the voltage across the resistor R1 and a voltmeter V2 is used to measure the voltage across the resistor R2.The voltmeter V1 is ±X% and the voltmeter V2 is +y% accurate. The voltmeter V1 reads 10 V and V2 reads 5 V. The absolute error of two voltmeters are the same and absolute error in total voltage V is 0.2 V.The values of X and Y (in %) respectively are:a)1%, 2%b)0.5%, 1%c)1%, 0.5%d)2%, 1%Correct answer is option 'A'. Can you explain this answer?
Question Description
Two resistors R1 and R2 are connected in series. The voltage across the series combination is V. A voltmeter V1 is used to measure the voltage across the resistor R1 and a voltmeter V2 is used to measure the voltage across the resistor R2.The voltmeter V1 is ±X% and the voltmeter V2 is +y% accurate. The voltmeter V1 reads 10 V and V2 reads 5 V. The absolute error of two voltmeters are the same and absolute error in total voltage V is 0.2 V.The values of X and Y (in %) respectively are:a)1%, 2%b)0.5%, 1%c)1%, 0.5%d)2%, 1%Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Two resistors R1 and R2 are connected in series. The voltage across the series combination is V. A voltmeter V1 is used to measure the voltage across the resistor R1 and a voltmeter V2 is used to measure the voltage across the resistor R2.The voltmeter V1 is ±X% and the voltmeter V2 is +y% accurate. The voltmeter V1 reads 10 V and V2 reads 5 V. The absolute error of two voltmeters are the same and absolute error in total voltage V is 0.2 V.The values of X and Y (in %) respectively are:a)1%, 2%b)0.5%, 1%c)1%, 0.5%d)2%, 1%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors R1 and R2 are connected in series. The voltage across the series combination is V. A voltmeter V1 is used to measure the voltage across the resistor R1 and a voltmeter V2 is used to measure the voltage across the resistor R2.The voltmeter V1 is ±X% and the voltmeter V2 is +y% accurate. The voltmeter V1 reads 10 V and V2 reads 5 V. The absolute error of two voltmeters are the same and absolute error in total voltage V is 0.2 V.The values of X and Y (in %) respectively are:a)1%, 2%b)0.5%, 1%c)1%, 0.5%d)2%, 1%Correct answer is option 'A'. Can you explain this answer?.
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