Solving Series Circuit Problems Using Ohm's Law
1. Determining the Number of Light Bulbs in a Series Circuit
Multiples light bulbs are connected in series across a 120.0 V source of emf. The current in the circuit is 1.25 A. If each light bulb has a resistance of 3.00 Ω, how many light bulbs are in the circuit?
2. Finding the Resistance of Bulb C in a Series Circuit
If the resistance of bulb A is 6 Ω, the resistance of bulb B is 18 Ω, and the equivalent resistance of the circuit is 120 Ω, what is the resistance of bulb C?
1) Since each bulb has a resistance of 3.00 Ω, we can calculate the number of bulbs: n = R/R_bulb = 96 Ω/3.00 Ω = 32 bulbs. There are 32 light bulbs in the circuit.
2) The total resistance is equal to the sum of individual resistances: R_C = 120 Ω - 6 Ω - 18 Ω = 96 Ω. The resistance of bulb C is 96 Ω.
In a series circuit, the total resistance is equal to the sum of individual resistances. Using Ohm's Law, we can find the total resistance:
R = V/I = 120.0 V/1.25 A = 96 Ω
Since each bulb has a resistance of 3.00 Ω, we can calculate the number of bulbs:
n = R/R_bulb = 96 Ω/3.00 Ω = 32 bulbs
Therefore, there are 32 light bulbs in the circuit.
In a series circuit, the total resistance is equal to the sum of individual resistances:
R_eq = R_A + R_B + R_C
Substituting the given values:
120 Ω = 6 Ω + 18 Ω + R_C
Solving for R_C:
R_C = 120 Ω - 6 Ω - 18 Ω = 96 Ω
Therefore, the resistance of bulb C is 96 Ω.
1. How is the number of light bulbs in a series circuit calculated? 2. What is the total resistance in a series circuit equal to? 3. How can Ohm's Law be used to determine the resistance of a bulb in a series circuit? 1. The number of light bulbs in a series circuit can be calculated by dividing the total resistance of the circuit by the resistance of each light bulb. 2. The total resistance in a series circuit is equal to the sum of the individual resistances of the components in the circuit. 3. Ohm's Law can be used to determine the resistance of a bulb in a series circuit by knowing the voltage and current in the circuit and calculating the ratio of voltage to current.