Calculating Resistance in a Series Circuit with Holiday Lights
Understanding Resistance in a Series Circuit
A string of holiday lights has eight bulbs with equal resistances connected in series. When the string of lights is connected to a 120 V outlet, the current through the bulbs is 0.08 A. We need to calculate the equivalent resistance of the circuit and the resistance of each individual bulb.
Calculating Equivalent Resistance
To find the equivalent resistance of the circuit, we can use Ohm's Law which states that resistance (R) is equal to voltage (V) divided by current (I). So, R = V/I. Using the given values, we get R = 120/0.08 = 1500 ohms. Therefore, the equivalent resistance of the circuit is 1500 ohms.
Calculating Resistance of Each Bulb
To find the resistance of each bulb, we can use the fact that the bulbs are connected in series, which means that the total resistance is the sum of the individual resistances. Since there are eight bulbs with equal resistances, we can divide the equivalent resistance by eight to get the resistance of each bulb. So, each bulb has a resistance of 1500/8 = 187.5 ohms. Therefore, the resistance of each bulb is 187.5 ohms.
A string of holiday lights has eight bulbs with equal resistances connected in series. When the string of lights is connected to a 120 V outlet, the current through the bulbs is 0.08 A. (a) What is the equivalent resistance of the circuit? (b) What is the resistance of each bulb?
Answer:
(a) The equivalent resistance of the circuit is 1500 ohms.
(b) The resistance of each bulb is 187.5 ohms.