when you connect an unknown resistor across the terminals of a 1.50 V AAA battery having a negligible internal resistance, you measure a current of 18.0 mA flowing through it .A)what is the resistance of the resistor. B) if you now place the resistor across the terminals of a 12.6 v car battery having no internal resistance,how much current will flow? .C)you now put the resistor across the terminal of an unknown battery of negligible internal resistance and measure the current of 0.453 A flowing through it, what is the potential difference across the terminals of the battery ?
Let's solve the problems step by step.
A) To find the resistance (R) of the unknown resistor, we can use Ohm's Law: V = I * R, where V is the voltage (1.50 V) and I is the current (18.0 mA = 0.018 A). Rearranging the equation, we have R = V / I.
Substituting the given values:
R = 1.50 V / 0.018 A
R = 83.33 Ω
Therefore, the resistance of the unknown resistor is 83.33 Ω.
B) Since the car battery has a voltage of 12.6 V and no internal resistance, the same resistor will experience a different current when connected to it. To calculate the current, we can again use Ohm's Law: I = V / R.
Substituting the given values:
I = 12.6 V / 83.33 Ω
I ≈ 0.151 A (rounded to three decimal places)
Therefore, approximately 0.151 A (or 151 mA) of current will flow through the resistor when connected to the car battery.
C) Now, let's calculate the potential difference across the terminals of the unknown battery. We know the current (0.453 A) and the resistance (83.33 Ω).
Using Ohm's Law: V = I * R.
Substituting the given values:
V = 0.453 A * 83.33 Ω
V ≈ 37.78 V (rounded to two decimal places)
Therefore, the potential difference across the terminals of the unknown battery is approximately 37.78 V.
To find the answers to these questions, we can use Ohm's Law, which states that the current flowing through a resistor is directly proportional to the voltage across it, and inversely proportional to its resistance. Ohm's Law equation is I = V / R, where I is the current, V is the voltage, and R is the resistance.
A) To find the resistance of the resistor when connected to the 1.50 V AAA battery, we can rearrange Ohm's Law equation to solve for R: R = V / I. Substituting the values, we have R = 1.50 V / 18.0 mA. Let's first convert milliamperes (mA) to amperes (A): 18.0 mA = 18.0 / 1000 A = 0.018 A. Now we can substitute the values in the equation: R = 1.50 V / 0.018 A. Simplifying this gives us the resistance: R ≈ 83.33 ohms.
B) To find the current flowing through the resistor when connected to the 12.6 V car battery, we can use Ohm's Law again: I = V / R. Substituting the values, we have I = 12.6 V / 83.33 ohms. Solving this gives us the current: I ≈ 0.151 A or 151 mA.
C) To find the potential difference across the terminals of the unknown battery when the resistor has a current of 0.453 A flowing through it, we can once again use Ohm's Law: V = I * R. Substituting the values, we have V = 0.453 A * 83.33 ohms. Solving this gives us the potential difference: V ≈ 37.5 V.
In summary:
A) The resistance of the resistor is approximately 83.33 ohms.
B) The current flowing through the resistor when connected to the 12.6 V car battery is approximately 151 mA.
C) The potential difference across the terminals of the unknown battery is approximately 37.5 V.