Q57P - Fundamentals Of Physics

Question

A 18 .0 W device has 9.00 V across it. How much charge goes through the device in 4.00 h ?

Step-by-Step Solution

Answer

The amount of charge goes through the device is $2.88\times {10}^{4}C$ .

Step 1: Identification of the given data

The given data can be listed below as: 

• Power of the device is, P = 18.0 W .
• Potential difference is, V = 9.00 V .
• Time interval is, $t=4 hr =1.44\times {10}^{4 }s$

Step 2: Understanding the concept of the charge

First, we need to find the current flowing through the device. Then finding the product of the current and time, we can estimate the amount of charge, Q. 

 

Formulae:

The electric power generated in the circuit is,

P = i x V                                                                                                                       … (i)

 

The electric current in the circuit is,

  $i=\frac{P}{V}$                                                                                                                         … (ii)

 

The current flowing through the area is,

$i=\frac{Q}{t}$                                                                                                                         … (iii)

 

The charge flowing through the area is,

$Q=it$                                                                                                                          … (iv)

Step 3: Calculation of the amount of charge

Substituting the given values in equation (ii), we can get the value of the current flowing as follows:

$$\begin{gathered} i=\frac{18.0W}{9.00 V} \\ =2.00A \end{gathered}$$

 

The amount of charge going through the device can be calculated using the current value in equation (iv) as follows:

$$\begin{gathered} Q=2.00A\times 1.44\times {10}^{4}s \\ =2.88\times {10}^{4}C \end{gathered}$$

 

Hence, the value of the charge entering into the device is $2.88\times {10}^{4}C$ .