A source of $e.m.f.$ $E = 15\,V$ and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = 1.2 t + 3$. Then, the total charge that will flow in first five second will be ............... $C$
Medium
Download our app for free and get started
$i = \frac{{dQ}}{{dt}}$ $ \Rightarrow $ $dQ = idt$ $ \Rightarrow $ $Q = \int_{\,{t_1}}^{\,{t_2}} i \,dt = \int_0^5 {(1.2t + 3)\,} dt$
$ = \left[ {\frac{{1.2{t^2}}}{2} + 3t} \right]_0^5 = 30\,C$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1View SolutionThe figure shows a network of four resistances and three batteries Mark the incorrect statement.
- 2Two bulbs $X$ and $Y$ having same voltage rating and of power $40\, watt$ and $60\, watt$ respectively are connected in series across a potential difference of $300\, volt$, thenView Solution
- 3A uniform wire of resistance $9$ $\Omega$ is cut into $3$ equal parts. They are connected in the form of equilateral triangle $ABC$. A cell of $e.m.f.$ $2\,V$ and negligible internal resistance is connected across $B$ and $C$. Potential difference across $AB$ is ............... $V$View Solution
- 4A potentiometer has uniform potential gradient. The specific resistance of the material of the potentiometer wire is $10^{-7} \, ohm-meter$ and the current passing through it is $0.1\, ampere$; cross-section of the wire is $10^{-6}\, m^2$. The potential gradient along the potentiometer wire isView Solution
- 5Assertion : The current density $\vec J$ at any point in ohmic resistor is in direction of electric field $\vec E$ at that point.View Solution
Reason : A point charge when released from rest in a region having only electrostatic field always moves along electric lines of force.
- 6What will be equivalent resistance of circuit between $x$ and $y$View Solution
- 7Three identical cells are connected in parallel across $A B$. Net emf across $A B$ is .......... $V$View Solution
- 8Find out current in $3\,\Omega $ resistance in given circuitView Solution
- 9The terminal potential difference of a cell when short-circuited is ($E$ = $E.M.F.$ of the cell)View Solution
- 10A $50 \,W$ bulb connected in series with a heater coil is put to an $AC$ mains. Now the bulb is replaced by a $100 \,W$ bulb. The heater output will ...........View Solution