
What is the resistance of the voltmeter shown in the circuit?
A.
B.
C.
D.

Answer
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Hint: In a series connection, the current is each element is equal to the supply current
whereas the supply voltage is equal to the sum of individual voltages
Ohm’s law states that for given physical conditions, the voltage drop across a particular element in a circuit is directly proportional to the current flowing through the element.
The mathematical expression is given as
Replacing the proportionality sign we get where R is the resistance of the element.
Complete step by step solution:
Since the voltmeter is connected in parallel across the , the voltage drop across the resistor is .
We know that in a series connection the voltage is the sum of voltage drops across each element.
Hence,
.
Now the current flowing through the is (by ohm’s law)
In a series connection the current flowing through each element is the same.
Hence, where represents the parallel connection of the voltmeter and the resistance.
The equivalent resistance of the connection( voltmeter and the resistance) is given as
using ohm’s law
So, the equivalent resistance of the combination is .
Let the resistance of the voltmeter be .
The parallel equivalent is given by
We have calculated the value of parallel equivalent to be
Substituting in the equation
Further solving this
Hence option B is correct.
Note: Voltmeters are devices with high resistances to allow least possible current to flow and are always connected in parallel to prevent heating of the circuit. Simplifying the circuit into smaller equivalents and then backward substituting the values is better than introducing new circuit variables for every branch in the circuit since it prevents the situation of handling multiple equations at the same time.
Ohm’s law states that for given physical conditions, the voltage drop across a particular element in a circuit is directly proportional to the current flowing through the element.
The mathematical expression is given as
Replacing the proportionality sign we get
Complete step by step solution:
Since the voltmeter is connected in parallel across the
We know that in a series connection the voltage is the sum of voltage drops across each element.
Hence,
Now the current flowing through the
In a series connection the current flowing through each element is the same.
Hence,
The equivalent resistance of the connection(
So, the equivalent resistance of the
Let the resistance of the voltmeter be
The parallel equivalent is given by
We have calculated the value of parallel equivalent to be
Substituting in the equation
Further solving this
Hence option B is correct.
Note: Voltmeters are devices with high resistances to allow least possible current to flow and are always connected in parallel to prevent heating of the circuit. Simplifying the circuit into smaller equivalents and then backward substituting the values is better than introducing new circuit variables for every branch in the circuit since it prevents the situation of handling multiple equations at the same time.
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