Chapter 28: Q. 4 (page 789)

The circuit of FIGURE Q28.4 has two resistors, with $R_{1} > R_{2}$ . Which of the two resistors dissipates the larger amount of power? Explain.

Short Answer

Expert verified

$R_{1}$ dissipates the larger amount of power. That is $P_{1} > P_{2}$

Step by step solution

Given information and formula used

Given :

In the following figure, $R_{1} > R_{2}$

Theory used :

Ohm's law, description of the relationship between current, voltage, and resistance. The amount of steady current through a large number of materials is directly proportional to the potential difference, or voltage, across the materials. That is

$∆ V_{R} = I \cdot R$

Determining which of the two resistors dissipates the larger amount of power.

When current passes through a resistor, it dissipates energy, and the rate at which this energy is dissipated is the power. $P_{R} = I ∆ V_{R}$ is the rate at which energy is transmitted from the current to the resistor.

We may get an alternate formula for the dissipated power from Ohm's law : $∆ V_{R} = I \cdot R$ .

The current flowing through the resistors and the circuit is the same in series.

As a result, $I$ is the same for $R_{1} and R_{2}$ . $P_{R}$ is proportional to resistance, as said earlier. Because the current is the same and $R_{1} > R_{2}$ , the power dissipated by $R$ is greater than the power dissipated by $R_{2}$ .