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Ohm's Law is a fundamental principle used to understand electric circuits. It establishes a relationship between voltage, current, and resistance in a simple way: \( V = I \times R \), where \( V \) is the voltage across the circuit, \( I \) is the current flowing through the circuit, and \( R \) is the resistance of the circuit. This formula helps us calculate the missing parameter if we know the other two.

For example, if the resistance \( R \) is known along with the voltage \( V \), the current \( I \) can be found by rearranging the formula to \( I = \frac{V}{R} \). On a basic level, it tells us how much current will flow through a resistor when a certain voltage is applied.

• If the resistance increases while the voltage remains constant, the current decreases.
• Conversely, if the resistance decreases, the current increases for the same voltage.

Understanding this simple law is crucial for analyzing more complex circuits, such as when resistors are added in series.

In series circuits, components are connected one after another, forming a single pathway for current flow. This means the same current flows through each component in the series. When you add resistors in series, like \( R_1 \) and \( R_2 \), the total resistance of the circuit becomes the sum of all individual resistances.

So, if initially, \( R_1 \) was the only resistor and \( R_2 \) was added in series, the total resistance becomes \( R_1 + R_2 \).

• This increases the total resistance of the circuit.
• With increased resistance, the current decreases, if the voltage stays the same (by Ohm's Law).

In series circuits, it’s important to remember that any increase in resistance affects the entire circuit's current, which in turn affects power dissipation.

Current reduction is a direct consequence of increasing the total resistance in a circuit without changing the voltage. Using Ohm's Law, we know that current \( I \) can be calculated as \( I = \frac{V}{R} \).

Now, when the resistance increases, like when \( R_2 \) is added to \( R_1 \) in series, the new resistance \( R_{total} = R_1 + R_2 \) is greater than the initial \( R_1 \). Thus, \( I = \frac{V}{R_{total}} \) produces a smaller current than \( I = \frac{V}{R_1} \).

• Less current means that less power is dissipated in the resistor, following the power dissipation formula \( P = I^2 R_1 \).
• Therefore, integrating more resistors in series leads to a decrease in power dissipation, as seen in the exercise's solution.

This principle is critical in designing circuits where controlling power dissipation is essential, such as in electrical safety management and device longevity.