A 50 V battery has an internal resistance r.
1 A
50 V
r
55 Ω
66 Ω
internal
resistance
What is the value of r?
Answer in units of Ω
To find the value of the internal resistance r, we can use Ohm's Law and the concept of voltage division.
Ohm's Law states that the current flowing through a circuit is equal to the voltage across the circuit divided by the total resistance of the circuit. In this case, we have a battery with a voltage of 50 V and an internal resistance of r. The current flowing through the circuit can be represented as:
I = V / R
Where:
I is the current in amperes,
V is the voltage in volts,
R is the total resistance in ohms.
However, to find the value of the internal resistance r, we need to consider the voltage division. When current flows through a circuit with multiple resistances, the voltage across each resistance is proportional to its value compared to the total resistance of the circuit.
In this case, the total resistance of the circuit can be represented as:
R_total = R_internal + R_load
Where:
R_internal is the internal resistance of the battery, and
R_load represents any additional resistance in the circuit.
Since we know the current flowing through the circuit is 1 A and the voltage across the battery is 50V, we can use these values in the voltage division equation:
V_internal = (R_internal / R_total) * V
Substituting the given values:
50V = (r / (r + R_load)) * 50V
To isolate the variable r, we can cross-multiply and solve for r:
50V * (r + R_load) = r * 50V
50r + 50R_load = 50r
50R_load = 0
Since 50R_load = 0, it implies that R_load is equal to 0. This means there is no additional resistance in the circuit apart from the internal resistance of the battery.
Therefore, the value of the internal resistance r is 0 Ω (ohms).