Assume that a 800 kΩkΩ resistor is connected between the 150 VV terminal and the common terminal. The voltmeter is then connected to an unknown voltage using the common terminal and the 300 VV terminal. The voltmeter reads 294 VV .What is the unknown voltage?

294 V

Explanation:

Given:

- The missing figure is attached:

- R_m is the resistance of the meter

- i_m is the current through meter = 1 mA

- v_m is the voltage drop across meter = 50 mV

Find:

Assume that a 800 kΩkΩ resistor is connected between the 150 VV terminal and the common terminal. The voltmeter is then connected to an unknown voltage using the common terminal and the 300 VV terminal. The voltmeter reads 294 VV .What is the unknown voltage?

Solution:

- We will first find the Resistance R_1 , R_2 , R_3  and R_m:

- The resistance R_m of meter can be calculated by Ohm's Law:

                          R_m = v_m / i_m

                          R_m = 50 / 1 = 50 ohms

- The resistance R_1 between common and 30 V:

                          R_1 + R_m = (potential difference) / i_m

                          R_1 = (potential difference) / i_m - R_m

                          R_1 = ( 30 - 0 )*10^3 - 50

                          R_1 = 29,950 ohms

- The resistance R_2 between 30 V and 150 V:

                          R_2= (potential difference) / i_m

                          R_2 = (potential difference) / i_m

                          R_2 = ( 50 - 30 )*10^3

                          R_2 = 20,000 ohms

- The resistance R_3 between 150 V and 300 V:

                          R_3= (potential difference) / i_m

                          R_3 = (potential difference) / i_m

                          R_3 = ( 300 - 150 )*10^3

                          R_3 = 150,000 ohms

- Now if we add 800 kilo ohms resistor across common and 150 V. The current in the circuit i will be as follows:

                          i = Potential difference / ( R_1 + 800,000 + R_2 + R_m)

                          R_eq = R_1 + 800,000 + R_2 + R_m

                                    = 29,950 + 50 + 800,000 + 20,000

                                    = 850,000 ohms

                          i = ( 150 - 0 ) / 850,000

                          i = 0.176447 mA

- The new galvanometer reading is 0.176447 mA. Now the voltmeter is connected at an unknown voltage V , between terminals 0 - 300 V and gives a reading of 294 V.

- A voltmeter is always connected in parallel to the circuit. Since our circuit contains load resistors then we known that reading on the voltmeter = 294

- The unknown voltage is the reading of volt-meter itself = 294 V

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