Final answer:
The answer is 1.1Ω. The internal resistance of the battery can be found by using Ohm's Law and calculating the voltage drop across the external resistor. Subtracting this from the total voltage provides the voltage across the internal resistance, which can then be used to find the internal resistance itself.
Step-by-step explanation:
We are dealing with a problem that involves finding the internal resistance of a battery in an electrical circuit. According to Ohm's Law, the total voltage (V) across a circuit is the sum of the voltage drop across the external resistance (VR) and the voltage drop across the internal resistance (Vint) of the battery.
We can express it with the equation V = IR + I(r), where I is the current, R is the external resistance, and r is the internal resistance of the battery.
In this problem, the total voltage supplied by the battery is 50 V, the current (I) is given as 4.5 A and the external resistance (R) is 10Ω.
To find the internal resistance (r) we first need to find the voltage drop across the external resistor (VR) which is
VR = IR
= 4.5 A × 10Ω
= 45 V.
Now, we use the total voltage to find the voltage across the internal resistance by subtracting the voltage across the external resistance from the total voltage:
Vint = V - VR
= 50 V - 45 V
= 5 V.
Knowing Vint and the current (I), we can find the internal resistance (r) using Ohm's Law (r = Vint / I), which yields
r = 5 V / 4.5 A
= 1.1Ω.