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.