Switch On and Shine Bright: Discover the Resistance of a Lamp
How can we find the resistance of a lamp when it is on?
Find the resistance of the lamp when it is on.
What is the cold resistance of the lamp?
Determine the cold resistance of the lamp.
What is the current through the lamp when it is turned on with a potential difference of 120 V?
Calculate the current through the lamp when it is turned on with 120 V.
Answer:
The resistance of the lamp when it is on is 316.22 ohms. The cold resistance of the lamp is 63.24 ohms. The current through the lamp when it is turned on with a potential difference of 120 V is 0.38 A.
Explanation:
(a) To find the resistance when the lamp is on, we can use Ohm's Law, which states that resistance is equal to voltage divided by current. In this case, the voltage is 117 V and the current is 0.37 A. So, the resistance is: R = V/I = 117 V / 0.37 A = 316.22 ohms (b) According to the question, the cold resistance is one fifth as large as the hot resistance. So, if we denote the hot resistance as R_hot, the cold resistance would be R_cold = R_hot / 5. To find the cold resistance, we need to first find the hot resistance. Using Ohm's Law again, we have: R_hot = V/I = 117 V / 0.37 A = 316.22 ohms Therefore, the cold resistance is: R_cold = R_hot / 5 = 316.22 ohms / 5 = 63.24 ohms (c) To find the current through the lamp when it is turned on with a potential difference of 120 V, we can use Ohm's Law once more. Using the resistance calculated in part (a), we have: I = V/R = 120 V / 316.22 ohms = 0.38 A