Question

The graph of current versus time in a wire is given by

If charge flows through the wire in $7.5s$ is ${q_1}$ and that flows through the wire in $15s$ is ${q_2}$, then ratio ${q_1}:{q_2}$ is
A. $2:1$
B. $1:2$
C. $4:1$
D. $1:4$
E. $1:3$

Answer 1

From the graph it is evident that the current remains the same in both the time stamps. So we can just use the current formula to calculate the charges in both the cases and then divide them to obtain the ratio.
Formulas used
$i = \dfrac{q}{t}$ where $i$ is the current flowing through the conductor, $q$ is the charge and $t$ is the time taken.

Complete step by step answer
Electric current is defined as the flow of electric charge (electrons) per unit time through a conducting medium. Its SI unit is Ampere and is symbolized by $A$. It is measured using a device called the ammeter.
The flow of electric current is due to the stream of charged particles such as electrons from a region of higher potential to a region of lower potential. This means that current can only flow through a medium when there is a potential difference present.
Now, we can solve the question given by using the definition of current which gives us the relation,
$i = \dfrac{q}{t}$ where $i$ is the current flowing through the conductor, $q$ is the charge and $t$ is the time taken.
On the graph given above we see that the value of current is constant from time $t = 7.5s$to $15s$ and beyond.
So, using the current equation we can write,
${q_1} = 6 \times 7.5$ $C$ where ${q_1}$is the charge at $t = 7.5s$
Similarly,
${q_2} = 6 \times 15C$ where ${q_2}$ is the charge at $t = 15s$
Dividing these two equations we get,
$\dfrac{{{q_1}}}{{{q_2}}} = \dfrac{{6 \times 7.5}}{{6 \times 15}}$
$\Rightarrow \dfrac{{{q_1}}}{{{q_2}}} = \dfrac{1}{2}$
${q_1}:{q_2} = 1:2$

Therefore, the correct option is B.

Note: In a conductor, the total current is due to the flow of electrons which are negative charge carriers. However, in case of semiconductors, the flow of current is due to both positive and negative carriers. Unlike conductors, semiconductors can only conduct electricity at very high temperatures. This is due to the fact that semiconductors have a negative coefficient of resistance with temperature. Which means that their resistance decreases with increase in temperature.