To calculate the total external resistance of the circuit, we need to find the internal resistance (r) of the battery.
Using the information provided, we can create the following equations:
Equation 1: V1 = EMF - (I * r) (1)
Equation 2: V2 = EMF - (I * 0) (2)
Where:
V1 is the reading from voltmeter V1
V2 is the reading from voltmeter V2
EMF is the electromotive force of the battery (12V)
I is the current flowing through the circuit
Since the resistance of the connecting wires and ammeter is negligible, the only resistance in the circuit is the internal resistance of the battery (r) and the external resistance (R). Therefore, the total resistance in the circuit can be written as:
Total Resistance (Rt) = r + R
By rearranging equation (1) and equation (2), we can express the current (I) in terms of V1 and V2:
I = (EMF - V1) / r (3)
I = (EMF - V2) / 0 (4)
Since the resistance of voltmeter V2 is negligible, equation (4) simplifies to:
I = EMF - V2 (5)
Substituting equations (3) and (5), we can equate the two expressions for I:
(EMF - V1) / r = EMF - V2
Let's solve for r:
(EMF - V1) = r * (EMF - V2)
r = (EMF - V1) / (EMF - V2) (6)
Now, we can calculate the internal resistance (r) using the values of V1, V2, and EMF.
Finally, we can find the total external resistance (Rt) by subtracting the internal resistance (r) from the total resistance (Rt):
Rt = r + R
Note: Without knowing the values of V1, V2, and EMF, we cannot determine the exact value of the total external resistance (Rt).