Consider a battery that has Vt = 12.0 V when it is not connected to a circuit. When a
10.0- resistor is connected with the battery, the potential difference across the battery’s terminals drops to 10.9 V. What is the internal resistance of the battery?
I = V/R = 10.9/10 = 1.09 Amps.
r = V/I = (12-10.9)/1.09 = 1.0 Ohm.
I = V/R = 10.9/10 = 1.09 Amps.
r = V/I = (12-10.9)/1.09 = 1.0 Ohm.
I = V/R = 10.9/10 = 1.09 Amps.
r = V/I = (12-10.9)/1.09 = 1.0 Ohm.
To find the internal resistance of the battery, we can use Ohm's Law and the concept of voltage division. Ohm's Law states that the current flowing through a resistor is directly proportional to the potential difference (voltage) across the resistor and inversely proportional to the resistance. The formula for Ohm's Law is:
V = IR
Where V is the voltage across the resistor, I is the current flowing through the resistor, and R is the resistance.
In our case, we know that the voltage across the battery's terminals drops from Vt (12.0 V) to 10.9 V when a 10.0-Ω resistor is connected. This voltage drop across the resistor (VR) is equal to the potential difference across the battery's terminals minus the potential difference across the internal resistance of the battery (Vint):
VR = Vt - Vint
We are given VR (10.9 V) and Vt (12.0 V), and we need to find Vint.
Now, using Ohm's Law, we know that the current flowing through the resistor is equal to VR divided by the resistance of the resistor (R):
I = VR / R
Since the resistance of the resistor (R) is given as 10.0 Ω, we can calculate the current (I).
Next, we can use voltage division to find the potential difference across the internal resistance of the battery (Vint). Voltage division states that the potential difference across a resistor in a series circuit is proportional to its resistance. The formula for voltage division is:
Vint = (Rint / (Rint + R)) * VR
Where Rint is the internal resistance of the battery.
We know VR (10.9 V), R (10.0 Ω), and Vint is what we need to find.
Now, using the formula for voltage division, we can substitute the values and calculate Vint. Once we have Vint, we can rearrange the formula to solve for Rint:
Rint = (Vint / VR) * R
Substituting the values of Vint and VR, we can calculate Rint, which will give us the internal resistance of the battery.