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 internal resistance of the batteries is negligible, what power is delivered to the bulb?

Verified step by step guidance

1. Step 1: Understand the problem setup. We have two batteries connected in series, each with an electromotive force (emf) of 1.5 V. This means the total voltage supplied by the batteries is the sum of their individual emfs.
2. Step 2: Calculate the total voltage supplied by the batteries. Since they are in series, the total voltage (V_total) is given by: $V_{\mathrm{total}}=1.5+1.5$
3. Step 3: Use Ohm's Law to find the current flowing through the circuit. Ohm's Law states that the current (I) is equal to the voltage (V) divided by the resistance (R). The formula is: $I=\frac{V_{\mathrm{total}}}{R}$, where R is the resistance of the bulb.
4. Step 4: Substitute the values into Ohm's Law. The resistance of the bulb is 17 Ω, and the total voltage is 3 V (from Step 2). So, the current is: $I=\frac{3}{17}$
5. Step 5: Calculate the power delivered to the bulb using the formula for electrical power: $P=V_{\mathrm{total}}I$. Substitute the values for V_total and I from the previous steps to find the power.

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 V.

Series Circuit

In a series circuit, components are connected end-to-end, so the same current flows through each component. The total voltage across the circuit is the sum of the voltages across each component. Here, the batteries are in series, providing a combined voltage of 3 V to the bulb.

Power in Electrical Circuits

Power in an electrical circuit is the rate at which energy is transferred or converted. It is calculated using the formula P = V^2/R, where P is power, V is voltage, and R is resistance. For the bulb with a resistance of 17 Ω and a voltage of 3 V, the power delivered can be calculated using this formula.