Question

Compute the heat generated while transferring $96000$ C of charge in two hours through a potential difference of $50{\text{V}}$.

Answer 1

Hint: First, we need to calculate the value of current from the given values of charge and time and then by using the value of current, we will find the amount of heat generated. The value of given time is in hours, so convert it into seconds.

Formula Used:
${\text{Current(i) = }}\dfrac{{{\text{Charge}}}}{{{\text{Time}}}}$
${\text{Heat(H) = V}} \times {\text{i}} \times {\text{t}}$

Complete step by step solution:
Charge (Q) = $96000{\text{C}}$
Time (t) = $2{\text{ hours = 2}} \times 3600{\text{ sec = 7200 sec}}$ [$1{\text{ hour = 3600 sec}}$]
Potential difference (V) = $50{\text{V}}$
We can find the value of current by using the formula
${\text{Current(i) = }}\dfrac{{{\text{Charge}}}}{{{\text{Time}}}} = \dfrac{{\text{Q}}}{{\text{t}}}$
By substituting the given values in the above formula, we get
$ \Rightarrow {\text{Current(i) = }}\dfrac{{96000}}{{{\text{7200}}}}$
$ \Rightarrow {\text{i = }}\dfrac{{120}}{9}$
Now, from the value of current obtained from the above calculation, we can calculate the quantity of heat generated by using the formula
${\text{Heat(H) = V}} \times {\text{i}} \times {\text{t}}$
By substituting the values in the above formula, we get
\[ \Rightarrow {\text{Heat(H) = 50}} \times \dfrac{{120}}{9} \times 720\]
\[ \Rightarrow {\text{H = 50}} \times {\text{120}} \times {\text{80}}\]
On further calculation, we get
\[
   \Rightarrow {\text{H = 480000 = 4}}{\text{.8}} \times {\text{1}}{{\text{0}}^5}{\text{ Joules}} \\
  {\text{ }} \\
 \]
Therefore, The quantity of heat generated is \[{\text{4}}{\text{.8}} \times {\text{1}}{{\text{0}}^5}{\text{ Joules}}\].

Additional Information:Electric current is generated due to the flow of electrons. When a potential difference is applied between two points of a conductor, the electrons will start moving and collide each other. During this process, some quantity of heat energy will be released. If the applied potential difference is more, then more quantity of heat energy will be liberated and vice versa.
If the resistance(r) of the conductor is given instead of potential difference, the heat generated can be found by the formula, ${\text{H = }}{{\text{i}}^2} \times {\text{r}} \times {\text{t}}$

Note: The question can be solved without using the given time. Instead of substituting the values in the current formula, directly substitute the formula of current in the heat generated formula
$ \Rightarrow {\text{H = V}} \times {\text{i}} \times {\text{t }}$
$ \Rightarrow {\text{H = V}} \times \dfrac{{\text{Q}}}{{\text{t}}} \times {\text{t}}$
$ \Rightarrow {\text{H = V}} \times {\text{Q}}$
So by substituting the values of V and Q in the above equation, we can directly get the value of the quantity of heat generated.