Q4Q - Fundamentals Of Physics

Question

Figure 26-18, shows plots of the current I through a certain cross section of a wire over four different time periods. Rank the periods according to the net charge that passes through the cross section during the period, greatest first.

Step-by-Step Solution

Answer

Ranking of periods according to the net charge passing through the cross section is $t_a=t_b=t_C>t_d$.

Step 1: The given data

Figure 26-18 is the graph of current Vs time.

Step 2: Understanding the concept of the period from current equation

We use the formula for current related to charge and period. Calculating the area under each curve, we can rank the periods according to the net charge that passes through the area.

 

Formula:

The current flowing through the circuit,$I=\frac{Q}{t}$                                                              …(i)

is the charge, and t is the time

Step 3: Calculation of the rank of periods according to their charge

Using the value of equation (i), we can get the below charge equation as follows:

Q=it

We can get the amount of charge passing by the number of squares under the curve.

For region a) we can write the charge equation that gives the period of this region as follows:

$$\begin{gathered} Q=2it \\ {t}_a=\frac{Q}{2i} \end{gathered}$$

For region b), we can write the charge equation that gives the period of this region as follows:

$$\begin{gathered} Q=i2t \\ {t}_b=\frac{Q}{2i} \end{gathered}$$

For region c), we can write the charge equation that gives the period of this region as follows:

$$\begin{gathered} Q=\frac{1}{2}\left(2i\right)\left(2t\right) \\ =2it \\ {t}_c=\frac{Q}{2i} \end{gathered}$$

For region d), we can write the charge equation that gives the period of this region as follows:

$$\begin{gathered} Q=\frac{1}{2}\left(2i\right)t-\frac{1}{2}\left(2i\right)t \\ =0 \\ {t}_d=0 \end{gathered}$$

Hence, we can rank periods according to net charge as$t_a=t_b=t_C>t_d$.