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Chapter 28: Problem 11

The voltage across two components in series is zero. Is it possible that the voltages across the individual components aren't zero? Give an example.

Short Answer

Expert verified
Yes, it's possible that the individual components have non-zero voltages even when the voltage across the series is zero. An example is if one component has a voltage of +V and another has a voltage of -V, resulting in a total voltage of zero.

Step by step solution

01

Understand the concept of voltage in series

In a series circuit, the total voltage is considered as the sum of the voltages across the individual components. Mathematically, this is expressed as \( V_{total} = V_{1} + V_{2} + V_{3} + ... + V_{n} \) where \( V_{total} \) is the total voltage, and \( V_{1} , V_{2} , V_{3} ... V_{n} \) are the voltages across the individual components.
02

Apply the concept to the given exercise

With the total voltage across the components given as zero, it means \( V_{total} = 0 \). Since this is a sum of the voltages across the individual components, this implies that the sum of voltages across the individual components is zero. Therefore, it's possible for the voltages across the individual components to be non-zero, provided their sum equals zero.
03

Give an example

For example, consider two components in series having voltages of +V and -V (in the presence of a voltage source). The positive and negative voltages imply the direction of the voltage drop. The total voltage across the two components can be calculated by adding up the two voltages. This will give \( V_{total} = +V + (-V) = 0 \). So, each component has a non-zero voltage across it, yet the total voltage across the two components is zero.

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