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
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
The voltmeter reading can be calculated using the formula for the total voltage in a series circuit, which is the sum of the individual voltages.
The voltage across a cell in a circuit is given by the formula V = E - Ir, where E is the emf of the cell, I is the current in the circuit, and r is the internal resistance of the cell.
However, in this case, we don't know the current in the circuit. But we can calculate it using Ohm's law, which states that the current in a circuit is equal to the total voltage (or emf) divided by the total resistance.
First, we calculate the total emf (E_total) and the total resistance (R_total) in the circuit:
E_total = E_A + E_B = 10V + 4V = 14V
R_total = r_A + r_B = 1.0Ω + 2.0Ω = 3.0Ω
Then, we calculate the current (I) in the circuit using Ohm's law:
I = E_total / R_total = 14V / 3.0Ω = 4.67A
Now, we can calculate the voltage across each cell:
V_A = E_A - Ir_A = 10V - 4.67A1.0Ω = 5.33V
V_B = E_B - Ir_B = 4V - 4.67A2.0Ω = -5.33V
The negative sign for V_B indicates that the direction of the current is opposite to the direction of the emf in cell B.
Finally, the reading on the voltmeter is the sum of the voltages across the two cells:
V_total = V_A + V_B = 5.33V - 5.33V = 0V
So, the reading on the voltmeter is 0V.
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