A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. If the batteries last for 5.0 h, what is the total energy delivered to the bulb?

Verified step by step guidance

1. First, understand that when batteries are connected in series, their emfs add up. Therefore, the total emf provided by the two batteries is 1.5 V + 1.5 V = 3.0 V.
2. Next, use Ohm's Law to find the current flowing through the circuit. Ohm's Law is given by: $I=\frac{V}{R}$, where $I$ is the current, $V$ is the voltage, and $R$ is the resistance. Substitute the values: $I=\frac{3.0}{17}$.
3. Calculate the power delivered to the bulb using the formula: $P=IV$, where $P$ is the power, $I$ is the current, and $V$ is the voltage. Use the current calculated in the previous step and the total voltage of 3.0 V.
4. To find the total energy delivered to the bulb, use the formula: $E=Pt$, where $E$ is the energy, $P$ is the power, and $t$ is the time. Substitute the power calculated in the previous step and the time of 5.0 hours, converting hours to seconds (1 hour = 3600 seconds).
5. Finally, perform the multiplication to find the total energy delivered to the bulb over the 5.0 hours. Remember to keep track of units and convert them appropriately to ensure the energy is in joules.

Key Concepts

Electromotive Force (EMF)

EMF is the voltage generated by a battery or power source when no current is flowing. It represents the energy provided per charge unit. In this question, each battery has an EMF of 1.5 V, and when connected in series, the total EMF is the sum of individual EMFs, resulting in 3.0 V.

Ohm's Law

Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is expressed as I = V/R. For the flashlight, the current can be calculated using the total EMF (3.0 V) and the bulb's resistance (17 Ω).

Energy Delivered

The energy delivered to a component in an electrical circuit is calculated using the formula E = P × t, where P is the power (P = V × I) and t is the time. In this scenario, the power can be determined using the total voltage and current, and the energy delivered over 5 hours can be calculated accordingly.