The maximum permissible current through a galvanometer (G) of resistance 10ohmams is 0.05A. A resistance (R) is used to convert G into a voltameter with a maximum reading of 100v . find the value of R and how it is connected to G an?
full scale voltage=.05*10=.5volts.
so for 100 volt, 99.5 volts=.05(10+RinSeries) solve for the series resistance.
99.5/.05=10+R=1990
R=1980 ohms
R=1980
To convert the galvanometer (G) into a voltameter with a maximum reading of 100V, we need to use a suitable shunt resistor (R) in parallel with the galvanometer.
The shunt resistor will divert most of the current away from the galvanometer, allowing only a fraction of the total current to pass through it. This will enable the galvanometer to measure the voltage across the shunt resistor and provide readings in volts.
Let's calculate the value of the shunt resistor and determine how it is connected to the galvanometer.
Given:
Resistance of the galvanometer (G) = 10 ohms
Maximum permissible current through the galvanometer (Ig) = 0.05A
Maximum reading of the voltameter (Vmax) = 100V
We can start by finding the shunt resistance (Rs) using the formula:
Rs = (G / Ig) - G
Rs = (10 / 0.05) - 10
Rs = (200 - 10)
Rs = 190 ohms
Therefore, the value of the shunt resistor (R) should be 190 ohms.
To connect the shunt resistor (R) to the galvanometer (G), we need to connect them in parallel. This means that one terminal of the shunt resistor and one terminal of the galvanometer should be connected together, and the remaining two terminals should be connected to the circuit where we want to measure the voltage.
Remember, the polarity of the shunt resistor should match the polarity of the galvanometer, as attaching it in reverse polarity will cause incorrect readings.
So, to summarize:
- The value of the shunt resistor (R) is 190 ohms.
- The shunt resistor (R) should be connected in parallel with the galvanometer (G).
- One terminal of the shunt resistor should be connected to one terminal of the galvanometer, while the other terminals should be connected to the circuit where you want to measure the voltage.
To convert a galvanometer into a voltmeter, a series resistor is connected to the galvanometer. This series resistor limits the current flowing through the galvanometer, thus enabling it to measure higher voltages.
To find the value of the series resistor (R) needed to convert the galvanometer into a voltmeter with a maximum reading of 100V, we need to use Ohm's law.
Let's break down the problem step by step:
Step 1: Determine the maximum current through the galvanometer (G).
The maximum permissible current through the galvanometer is given as 0.05A.
Step 2: Calculate the resistance required to limit the current through G.
Using Ohm's law (V = IR), where V is the voltage across G and I is the current through G, we can calculate the resistance required.
Resistance (R_galvanometer) = V_galvanometer / I_galvanometer
Since a galvanometer is a sensitive current measuring device, we can assume that its resistance is much lower than R in the circuit.
Step 3: Calculate the value of R.
To convert the galvanometer into a voltmeter with a maximum reading of 100V, the total resistance (R_total) in the circuit should be equal to the resistance of G plus the series resistance (R).
R_total = R_galvanometer + R
Given that R_galvanometer (G) = 10 ohms, we can substitute this into the equation:
R_total = 10 ohms + R
Since the maximum current through the galvanometer is 0.05A, we can also use Ohm's law to calculate the maximum voltage across the total resistance:
V_total = I_max * R_total
V_total = 100V
Substituting the values into the equation:
100V = 0.05A * (10 ohms + R)
Simplifying the equation:
100V = 0.5 + 0.05A * R
Rearranging:
0.05A * R = 100V - 0.5V
0.05A * R = 99.5V
Dividing both sides by 0.05A:
R = 99.5V / 0.05A
R = 1990 ohms (rounded to the nearest whole number)
So, the value of R is 1990 ohms, and it should be connected in series with the galvanometer (G) to convert it into a voltmeter with a maximum reading of 100V.