Chapter 2, Problem 1P

Determine the current and power dissipated in the resistor in Fig. P2.1.

To determine

The current and power dissipated in the resistor.

Answer to Problem 1P

The current flowing in the circuit is $0.75\text{ A}$ and the power dissipated in the resistor is $6.75\text{ W}$ .

Explanation of Solution

Concept used:

Write the expression for the current.

  $i=\frac{v}{R}$    ..........(1)

Here, $i$ is the current flowing in the circuit, $v$ is the voltage across the resistor, $R$ is the resistance.

Write the expression for the power dissipated in the resistor.

  $p=i^{2}R$    ..........(2)

Here, $p$ is the power dissipated in the resistor.

Calculation:

The circuit diagram is drawn as shown in Figure 1.

Substitute $9\text{ V}$ for $v$ and $12\Omega$ for $R$ in equation (1).

  $\begin{array}{c}i=\frac{9\text{ V}}{12\Omega }\\ =\frac{3}{4}\text{}\text{ A}\\ =0.75\text{ A}\end{array}$

Therefore, the current flowing in the circuit is $0.75\text{ A}$ .

Substitute $0.75\text{ A}$ for $i$ and $12\Omega$ for $R$ in equation (2).

  $\begin{array}{c}p={\left(0.75\text{ A}\right)}^2\left(12\Omega \right)\\ =\left(0.5625\right)\left(12\right)\text{ W}\\ =6.75\text{ W}\end{array}$

Therefore, the power dissipated in the resistoris $6.75\text{ W}$ .

Conclusion:

Thus, the current flowing in the circuit is $0.75\text{ A}$ and the power dissipated in the resistor is $6.75\text{ W}$ .