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Chapter 7: Problem 24

Two \(1.5\) -volt batteries are connected in series in an electric circuit. Use the concept of energy to explain why this combination is equivalent to a single 3-volt battery. When connected in parallel, what are two \(1.5\) -volt batteries equivalent to?

Short Answer

Expert verified
Answer: Connecting two 1.5-volt batteries in series results in the addition of their voltages, providing a total of 3 volts, which indicates that they supply the same amount of energy as a single 3-volt battery. When connecting two 1.5-volt batteries in parallel, the equivalent voltage remains at 1.5 volts, but with an increased current capacity or longer battery life.

Step by step solution

01

Understand the concept of voltage and energy in electric circuits

In an electric circuit, a battery provides electrical energy to the circuit. This energy is measured in volts (V). The voltage of a battery represents the electric potential difference between its positive and negative terminals. This potential difference determines how much energy is transferred per unit charge (Coulombs) through the circuit.
02

Explain the combination of two 1.5-volt batteries connected in series

When two batteries are connected in series, their voltages are added up. The total voltage of the circuit is equal to the sum of the individual battery voltages. In this case, we have two 1.5-volt batteries connected in series. So, the total voltage of the circuit is: \(V_{total} = V_{1} + V_{2} = 1.5V + 1.5V = 3V\) As the total voltage represents the total energy supplied by the batteries, the combination of two 1.5-volt batteries connected in series is equivalent to a single 3-volt battery, as they both supply the same amount of energy to the circuit.
03

Explain the combination of two 1.5-volt batteries connected in parallel

When two batteries are connected in parallel, their voltages remain the same, and the total voltage of the circuit is equal to the individual battery voltages. However, the current supplied by each battery will be divided between them, resulting in a longer battery life or higher current capacity for the circuit. In this case, we have two 1.5-volt batteries connected in parallel. So, the total voltage of the circuit remains the same as the individual battery voltage: \(V_{total} = V_{1} = V_{2} = 1.5V\) Therefore, the combination of two 1.5-volt batteries connected in parallel is still equivalent to a single 1.5-volt battery in terms of voltage, but with an increased current capacity or longer battery life.

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