Ohm's Law and Incandescent Lamp Calculation
What is the relationship between the resistance of a 100 W incandescent lamp when cold and hot?
a) What is the lamp current and hot resistance when placed across a 120 V line?
b) What is the cold resistance of this lamp?
c) What is the instantaneous current through the lamp at the moment it is switched on?
d) What power does the lamp dissipate at this instant?
Relationship between Cold and Hot Resistance
The hot resistance is 12 times the cold resistance. This means that the resistance of the lamp when illuminated is 12 times higher compared to when it is not lit up.
Lamp Current and Hot Resistance Calculation
When the lamp is placed across a 120 V line, the lamp current and hot resistance can be calculated using Ohm's Law. The lamp current is determined by the formula I = V/R, where V is the voltage and R is the resistance.
Cold Resistance Calculation
The cold resistance of the lamp can be found by knowing that it is 1/12 of the hot resistance. Let's assume the cold resistance is R_c. Therefore, the hot resistance would be 12 times the cold resistance, which is 12R_c.
Instantaneous Current Calculation
The instantaneous current through the lamp at the moment it is switched on can be determined using Ohm's Law. By knowing the voltage across the lamp (120 V) and the resistance when hot (12R_c), we can calculate the instantaneous current.
Power Dissipation Calculation
The power dissipated by the lamp at the moment it is switched on can be calculated using the formula P = VI, where P is power, V is voltage, and I is current. With the voltage and current values known, we can find the power dissipated by the lamp.
Ohm's Law is a fundamental principle in physics that relates the voltage, current, and resistance in an electrical circuit. In the case of a 100 W incandescent lamp, the relationship between its cold and hot resistance is important for understanding its behavior when connected to a power source.
When the lamp is extinguished (cold), its resistance is only 1/12 of its resistance when illuminated (hot). This means that the resistance of the lamp increases significantly when it is lit up, resulting in a higher current flow through the circuit.
To calculate the lamp current and hot resistance when the lamp is connected to a 120 V line, Ohm's Law can be applied. By substituting the voltage and resistance values into the formula I = V/R, we can determine the current flowing through the lamp and the resistance when hot.
Furthermore, the cold resistance of the lamp can be found by considering that it is 1/12 of the hot resistance. By assuming a value for the cold resistance and calculating the hot resistance using this ratio, we can determine the resistance of the lamp when it is not illuminated.
When the lamp is switched on, the instantaneous current through the lamp can be calculated by applying Ohm's Law with the voltage across the lamp and the resistance when hot. This helps us understand the initial current flow through the circuit when the lamp is turned on.
Lastly, the power dissipated by the lamp at this instant can be calculated using the formula P = VI, where the voltage and current values are known. This provides insight into the amount of power consumed by the lamp as soon as it is switched on.