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A galvanometer of range 10 mA has a coil of resistance 1 Ω. To use it as a voltmeter of range 10 V, the resistance that must be connected in series with it, is
- a)9 Ω
- b)99 Ω
- c)999 Ω
- d)1000 Ω
Correct answer is option 'C'. Can you explain this answer?
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A galvanometer of range 10 mA has a coil of resistance 1 . To use it a...
Galvanometer as a voltmeter
To use a galvanometer as a voltmeter, we need to connect a resistance in series with it. This additional resistance is known as a shunt resistor. The value of the shunt resistor determines the range of the voltmeter.
Galvanometer specifications
In this case, we have a galvanometer with a range of 10 mA and a coil resistance of 1 Ω. This means that when a current of 10 mA flows through the coil, the deflection of the galvanometer will be maximum.
Calculating the shunt resistance
To convert the galvanometer into a voltmeter of range 10 V, we need to calculate the shunt resistance required.
The formula to calculate the shunt resistance is given by:
Rshunt = (Rg × (Vrange - Vg)) / Ig
Where:
Rshunt = Shunt resistance
Rg = Galvanometer resistance
Vrange = Desired voltmeter range
Vg = Galvanometer voltage for full-scale deflection
Ig = Galvanometer current for full-scale deflection
Calculating the shunt resistance for a range of 10 V
In this case, the desired voltmeter range is 10 V. We know that the galvanometer has a range of 10 mA, which means the galvanometer current for full-scale deflection (Ig) is 10 mA.
To calculate the galvanometer voltage for full-scale deflection (Vg), we can use Ohm's Law:
Vg = Ig × Rg
Substituting the given values:
Vg = 10 mA × 1 Ω = 0.01 V
Now we can calculate the shunt resistance:
Rshunt = (1 Ω × (10 V - 0.01 V)) / 10 mA
Rshunt = (1 Ω × (9.99 V)) / 10 mA
Rshunt = (9.99 Ω × 1000 Ω/1 Ω) = 9990 Ω
Therefore, the resistance that must be connected in series with the galvanometer to use it as a voltmeter of range 10 V is 9990 Ω, which is option 'C'.
To use a galvanometer as a voltmeter, we need to connect a resistance in series with it. This additional resistance is known as a shunt resistor. The value of the shunt resistor determines the range of the voltmeter.
Galvanometer specifications
In this case, we have a galvanometer with a range of 10 mA and a coil resistance of 1 Ω. This means that when a current of 10 mA flows through the coil, the deflection of the galvanometer will be maximum.
Calculating the shunt resistance
To convert the galvanometer into a voltmeter of range 10 V, we need to calculate the shunt resistance required.
The formula to calculate the shunt resistance is given by:
Rshunt = (Rg × (Vrange - Vg)) / Ig
Where:
Rshunt = Shunt resistance
Rg = Galvanometer resistance
Vrange = Desired voltmeter range
Vg = Galvanometer voltage for full-scale deflection
Ig = Galvanometer current for full-scale deflection
Calculating the shunt resistance for a range of 10 V
In this case, the desired voltmeter range is 10 V. We know that the galvanometer has a range of 10 mA, which means the galvanometer current for full-scale deflection (Ig) is 10 mA.
To calculate the galvanometer voltage for full-scale deflection (Vg), we can use Ohm's Law:
Vg = Ig × Rg
Substituting the given values:
Vg = 10 mA × 1 Ω = 0.01 V
Now we can calculate the shunt resistance:
Rshunt = (1 Ω × (10 V - 0.01 V)) / 10 mA
Rshunt = (1 Ω × (9.99 V)) / 10 mA
Rshunt = (9.99 Ω × 1000 Ω/1 Ω) = 9990 Ω
Therefore, the resistance that must be connected in series with the galvanometer to use it as a voltmeter of range 10 V is 9990 Ω, which is option 'C'.
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A galvanometer of range 10 mA has a coil of resistance 1 . To use it as a voltmeter of range 10 V, the resistance that must be connected in series with it, isa)9 b)99 c)999 d)1000 Correct answer is option 'C'. Can you explain this answer?
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