An infinite sequence of resistance is shown in the figure. The resultant resistance between $A$ and $B$ will be, when ${R_1} = 1\,ohm$ and ${R_2} = 2\,ohm$ ............. $\Omega$
A
Infinity
B$1$
C$2$
D$1.5$
Medium
Download our app for free and get started
C$2$
c Let the resultant resistance be $R$. If we add one more branch, then the resultant resistance would be the same because this is an infinite sequence.
$\therefore \frac{{R{R_2}}}{{R + {R_2}}} + {R_1} = R \Rightarrow 2R + R + 2 = {R^2} + 2R$
$ \Rightarrow {R^2} - R - 2 = 0 \Rightarrow R = - 1$ or $R = 2\,ohm$
Download our app
and 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.*
Two resistances ${R_1}$ and ${R_2}$ are joined as shown in the figure to two batteries of $e.m.f.$ ${E_1}$ and ${E_2}$. If ${E_2}$ is short-circuited, the current through ${R_1}$ is
Voltmeters $V_1$ and $V_2$ are connected in series across a $D.C.$ line. $V_1$ reads $80\, volts$ and has a per volt resistance of $200 \,\Omega$. $V_2$ has a total resistance of $32 \,kilo-ohms$. The line voltage is .............
An electric kettle has two coils. When one of these is switched on, the water in the kettle boils in $6\,\min$ . When the other coil is switched on, the water boils in $3\,\min$. If the two coils are connected in series, the time taken to boil the water in the kettle is ............. $min$
The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2 \,\Omega$. The value of internal resistance of each cell is ............ $\Omega$
The charge flowing through a resistance $R$ varies with time $t$ as $ Q=at-bt^2 $ where $a$ and $b$ are positive constants . The total heat produced in $R$ is
A current of $10\, amp$ is passing through a metallic wire of cross sectional area $4 \times 10^{-6}\, m ^{2}$. If the density of the aluminum conductor is $2.7\, gm / cc$ considering aluminum gives $1$ electrons per atom for conduction find the drift speed of the electrons is ......... $\times 10^{-4} \,m / s$ if molecular weight of aluminum is $27 \,gm$.