A circuit contains sic 60-W lamps with a resistance of 240-ohm each and a 10.0-ohm heater connected in parallel. The voltage across the circuit is 120 V. Find the current in the circuit for the following situations::::
a. four lamps are turned on
b. all of the lamps are turned on
c. six lamps and the heater are operating.
In each case, add the currents of all of the operating lamps and heater.
For the lamps, the current drawn by each ont that is "on" is I = V/R
= 120/ 240 = 0.5 A
For the heater, the current drawn is 120/10 = 12 A
To find the current in the circuit for each situation, we need to use Ohm's Law, which states that the current flowing through a circuit is equal to the voltage across the circuit divided by the total resistance.
First, let's find the total resistance of the circuit for each situation:
a. Four lamps are turned on:
Since four lamps are turned on, the total resistance of the lamps in parallel can be found using the formula:
1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + 1/R_4
where R_1, R_2, R_3, R_4 are the resistances of each lamp.
Given that the resistance of each lamp is 240 ohms, we have:
1/R_total = 1/240 + 1/240 + 1/240 + 1/240 = 4/240 = 1/60
R_total = 60 ohms
The resistance of the heater remains the same, which is 10 ohms.
b. All of the lamps are turned on:
Following the same calculation, the total resistance of all six lamps can be found as:
1/R_total = 1/240 + 1/240 + 1/240 + 1/240 + 1/240 + 1/240 = 6/240 = 1/40
R_total = 40 ohms
c. Six lamps and the heater are operating:
To find the total resistance for this situation, we add the resistance of the heater to the resistance calculated in part b:
R_total = R_heater + R_lamps_in_parallel = 10 + 40 = 50 ohms.
Now, we can calculate the current using Ohm's Law (V = I * R):
a. Four lamps are turned on:
I = V / R_total = 120 V / 60 ohms = 2 A
b. All of the lamps are turned on:
I = V / R_total = 120 V / 40 ohms = 3 A
c. Six lamps and the heater are operating:
I = V / R_total = 120 V / 50 ohms = 2.4 A