What is the internal resistance of a 15.0 V car battery whose terminal voltage drops to 13.40 V when the starter draws 50.1 A?

What is the resistance of the starter?

To find the internal resistance of the car battery, we can use Ohm's Law, which states that the voltage across a resistor is equal to the current flowing through it multiplied by its resistance.

In this case, we know the terminal voltage (Vt) and the current (I) drawn by the starter. The terminal voltage (Vt) is the voltage across the car battery when the starter is running.

Using Ohm's Law, we can write:

Vt = E - IR

Where E is the emf (electromotive force) or the open circuit voltage of the battery, and R is the internal resistance of the battery.

Rearranging the equation, we get:

R = (E - Vt) / I

Substituting the known values:

E = 15.0 V (given),
Vt = 13.40 V (given),
I = 50.1 A (given).

Now, we can calculate the internal resistance (R) of the car battery:

R = (15.0 V - 13.40 V) / 50.1 A
R = 1.60 V / 50.1 A
R ≈ 0.03194 Ω

Therefore, the internal resistance of the car battery is approximately 0.03194 ohms.

Now, to find the resistance of the starter, we can use Ohm's Law again.

Ohm's Law formula is: V = IR

We know the current (I) drawn by the starter is 50.1 A (given), and the terminal voltage (V) across the starter is equal to the voltage drop in the car battery, which is 13.40V (given).

Therefore, the resistance of the starter (R) can be calculated as:

R = V / I
R = 13.40 V / 50.1 A
R ≈ 0.267 ohms

Therefore, the resistance of the starter is approximately 0.267 ohms.

To find the internal resistance of the car battery, we can use Ohm's law, which states that V = I * R, where V is the voltage, I is the current, and R is the resistance.

In this case, we know the terminal voltage (V) and the current (I). We need to find the resistance (R). Rearranging the equation, we get R = V / I.

Given:
Terminal voltage (V) = 13.40 V
Current (I) = 50.1 A

Calculating the internal resistance of the car battery:
R = V / I
R = 13.40 V / 50.1 A
R ≈ 0.267 ohms

The internal resistance of the car battery is approximately 0.267 ohms.

Now, to find the resistance of the starter, we can use the formula R = V / I again, but this time we need to use the terminal voltage and the current drawn by the starter.

Given:
Terminal voltage (V) = 13.40 V
Current (I) = 50.1 A

Calculating the resistance of the starter:
R = V / I
R = 13.40 V / 50.1 A
R ≈ 0.267 ohms

Therefore, the resistance of the starter is approximately 0.267 ohms.