Final answer:
The value of the external resistor R connected to a battery with an emf of 6.00 V, when the terminal voltage is 5.90 V and the current is 0.14 A, is calculated to be 0.714 ohms.
Step-by-step explanation:
To determine the value of the external resistor (R) connected to a battery with given electromotive force (emf) and internal resistance (r), you can use the provided information about the terminal voltage and current running through the circuit.
When a battery with an emf of 6.00 V is connected to a resistor and the terminal voltage is measured to be 5.90 V with a current of 0.14 A running through it, we apply the formula for the terminal voltage of a battery, which is V = emf - Ir, where I is the current.
Using the given information:
- emf = 6.00 V
- Terminal Voltage (V) = 5.90 V
- Current (I) = 0.14 A
Plug these values into the equation:
5.90 V = 6.00 V - 0.14 A * r
Solving this equation for r gives:
r = (6.00 V - 5.90 V) / 0.14 A
r = 0.10 V / 0.14 A
r = 0.714 Ω
The value of the external resistor (R) that is connected to the battery is therefore 0.714 ohms.