The voltage across the terminals of a 8.90 V battery is 8.00 V when the battery is connected to a 50.0 \Omega load.What is the battery's internal resistance?
8.9/(50+Ri) = 8/50
solve for Ri
To find the battery's internal resistance, we need to use the formula that relates the voltage across the terminals of a battery to its internal resistance and the load resistance. This formula is known as the "voltage divider formula":
V = E - Ir,
where:
V is the voltage across the terminals of the battery,
E is the battery's electromotive force (EMF) or voltage when no current is flowing,
I is the current flowing through the circuit, and
r is the internal resistance of the battery.
In this case, we know the following values:
V = 8.00 V (voltage across the terminals of the battery when connected to the load)
E = 8.90 V (battery's electromotive force)
R = 50.0 Ω (load resistance)
Using the voltage divider formula, we can rearrange the equation to solve for the internal resistance:
r = (E - V) / I.
Since we know the values of V and E, we need to find the value of I to calculate the internal resistance.
To find the current I, we can use Ohm's Law, which states that the current flowing through a circuit is equal to the voltage across the circuit divided by the resistance.
So, I = V / R.
Substituting the known values, we get:
I = 8.00 V / 50.0 Ω = 0.16 A.
Now, we can substitute the values of V, E, and I into the equation for the internal resistance:
r = (8.90 V - 8.00 V) / 0.16 A = 5.63 Ω.
Therefore, the battery's internal resistance is approximately 5.63 Ω.