First, a set of ${n}$ equal resistors of $10\; \Omega$ each are connected in series to a battery of emf $20\; {V}$ and internal resistance $10\; \Omega .$ A current $I$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased $20$ times, then the value of $n$ is .... .
JEE MAIN 2021, Diffcult
Download our app for free and get started
In series
${R}_{{eq}}={nR}=10 {n}$
${i}_{{s}}=\frac{20}{10+10 {n}}=\frac{2}{1+{n}}$
in parallel
${R}_{{eq}}=\frac{10}{{n}}$
${i}_{{p}}=\frac{20}{\frac{10}{{n}}+10}=\frac{2 {n}}{1+{n}}$
$\frac{{i}_{{p}}}{{i}_{{s}}}=20$
$\frac{\left(\frac{2 {n}}{1+{n}}\right)}{\left(\frac{2}{1+{n}}\right)}=20$
${n}=20$
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
- 1Current density in a cylindrical wire of radius $R$ is given as $J =$ $\left\{ {\begin{array}{*{20}{c}}View Solution
{{J_0}\left( {\frac{x}{R} - 1} \right)\,\,for\,\,0 \leqslant x < \frac{R}{2}} \\
{{J_0}\frac{x}{R}\,\,\,\,for\,\,\,\frac{R}{2} \leqslant x \leqslant R}
\end{array}} \right.$The current flowing in the wire is: - 2View SolutionIn a sensitive meter bridge apparatus the bridge wire should possess
- 3In the circuit shown below (on the left) the resistance and the emf source are both variable. The graph of seven readings of the voltmeter and the ammeter ( $V$ and $I$, respectively) for different settings of resistance and the emf, taken at equal intervals of time $\Delta t$, are shown below (on the right) by the dots connected by the curve $E F G H$. Consider the internal resistance of the battery to be negligible and the voltmeter an ammeter to be ideal devices. (Take, $R_0 \equiv \frac{V_0}{I_0}$ ).View Solution
Then, the plot of the resistance as a function of time corresponding to the curve $E F G H$ is given by
- 4Two bulbs of $100\, W$ and $200\, W$ working at $220$ $volt$ are joined in series with $220$ $volt$ supply. Total power consumed will be approximately ........... $watt$View Solution
- 5The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... $\%$.View Solution
- 6Eight resistances each of resistance $5\,\Omega $ are connected in the circuit as shown in figure. The equivalent resistance between $A$ and $B$ isView Solution
- 7The resistivity $(\rho)$ of semiconductor varies with temperature. Which of the following curve represents the correct behaviourView Solution
- 8A wire of resistance $4 \,\Omega$ is stretched to twice its original length. The resistance of stretched wire would be ........... $\Omega$View Solution
- 9In a conductor, if the number of conduction electrons per unit volume is $8.5 \times 10^{28}\, m^{-3}$ and mean free time is $25\,fs$ (femto second), its approximate resistivity is $\left( {{m_e} = 9.1 \times {{10}^{ - 31}}\,kg} \right)$View Solution
- 10$10$ resistors, each of resistance $R$ are connected in series to a battery of $emf$ $E$ and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased $n$ times. The value of $n$ is :View Solution