A current of 0.5 A flows when a battery of emf 6V is connected to an 11 Ω resistor. What is the internal resistance of the battery?
Show work.
THANK YOU!
yes
well, the total resistance is E/I = 6/0.5 = 12Ω
so, what do you think?
To find the internal resistance of the battery, we can use Ohm's Law and the equation for the total resistance in a circuit.
Ohm's Law states that the current flowing through a resistor is equal to the voltage across the resistor divided by the resistance:
I = V/R
Where:
I is the current (in Amperes)
V is the voltage (in Volts)
R is the resistance (in Ohms)
In this case, the current I is given as 0.5 A and the resistance R is given as 11 Ω. We need to solve for the voltage V.
Rearranging Ohm's Law to solve for V:
V = I * R
Substituting the given values:
V = 0.5 A * 11 Ω
V = 5.5 V
The voltage across the resistor is 5.5 V.
Next, we can use the equation for the total voltage in a circuit:
Emf = V + Ir
Where:
Emf is the electromotive force or voltage of the battery (in Volts)
V is the voltage across the resistor (in Volts)
I is the current through the circuit (in Amperes)
r is the internal resistance of the battery (in Ohms)
Substituting the given values:
6 V = 5.5 V + 0.5 A * r
Rearranging to solve for r:
0.5 A * r = 6 V - 5.5 V
0.5 A * r = 0.5 V
Dividing both sides of the equation by 0.5 A:
r = 0.5 V / 0.5 A
r = 1 Ω
Therefore, the internal resistance of the battery is 1 Ω.
To find the internal resistance of the battery, you can use Ohm's Law, which states that the current flowing through a conductor is equal to the voltage across the conductor divided by its resistance.
Given that the current (I) is 0.5 A, the voltage (V) of the battery is 6V, and the resistance (R) of the external resistor connected to the battery is 11 Ω, we can apply Ohm's Law as follows:
I = V / (R + r)
Where "r" represents the internal resistance of the battery.
Substituting the given values into the equation:
0.5 A = 6V / (11 Ω + r)
Multiplying both sides of the equation by (11 Ω + r):
(11 Ω + r) * 0.5A = 6V
Expanding the left side of the equation:
5.5 Ω * A + r * 0.5A = 6V
Since the terms on the left side have the same units (Ampere), we can combine them:
(5.5 Ω + 0.5r) * A = 6V
Now, we can solve the equation for "r" by simplifying and rearranging the equation:
0.5r = 6V - 5.5 Ω * A
0.5r = 6V - 5.5V
0.5r = 0.5V
Dividing both sides by 0.5:
r = 0.5V / 0.5
r = 1 Ω
Therefore, the internal resistance of the battery is 1 Ω.
In summary, to find the internal resistance of the battery, you need to apply Ohm's Law by rearranging the equation and solving for "r" using the given values of current, voltage, and external resistor.