(c) The voltmeter is used in another circuit that contains two secondary cells.Vcell Bcell A10 V 1.0 Ω2.0 Ω4.0 VCell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 Vand an internal resistance of 2.0 Ω.Calculate the reading on the voltmeter.
Question
(c) The voltmeter is used in another circuit that contains two secondary cells.Vcell Bcell A10 V 1.0 Ω2.0 Ω4.0 VCell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 Vand an internal resistance of 2.0 Ω.Calculate the reading on the voltmeter.
Solution
To calculate the reading on the voltmeter, we need to find the total voltage in the circuit. This is the sum of the voltages across each cell, which is determined by the emf of each cell and the current flowing through it.
The total resistance in the circuit is the sum of the internal resistances of the two cells, which is 1.0 Ω + 2.0 Ω = 3.0 Ω.
The total emf in the circuit is the sum of the emfs of the two cells, which is 10 V + 4 V = 14 V.
The current in the circuit can be found using Ohm's law, which states that the current is equal to the voltage divided by the resistance. So, the current is 14 V / 3.0 Ω = 4.67 A.
The voltage across each cell is equal to the emf of the cell minus the product of the current and the internal resistance of the cell (V = E - Ir).
For cell A, the voltage is 10 V - (4.67 A * 1.0 Ω) = 5.33 V. For cell B, the voltage is 4 V - (4.67 A * 2.0 Ω) = -5.33 V.
The negative sign indicates that the direction of the current is opposite to the direction of the emf. However, the voltmeter only measures the magnitude of the voltage, not its direction. So, the reading on the voltmeter is the sum of the magnitudes of the voltages across the two cells, which is 5.33 V + 5.33 V = 10.66 V.
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