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A wire of length ' $r$ ' and resistance $100 \Omega$ is divided into $10$ equal parts. The first $5$ parts are connected in series while the next $5$ parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:
Refer to the circuit shown. What will be the total power dissipation in the circuit if $P$ is the power dissipated in $R_1$ ? It is given that $R_2=4 R_1$ and $R_3=12 R_1$ are .......... $P$
In the circuit shown below $E_1\, =4.0\, V$, $R_1\, = 2\,\Omega$, $E_2\, = 6.0\, V$, $R_2\, = 4\,\Omega$ and $R_3\, = 2\,\Omega$. The current $I_1$ is ............... $\mathrm{A}$
A metal wire of resistance $3\,\Omega $ is elongated to make a uniform wire of double its previous length. The new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle $60^o$ at the centre, the equivalent resistance between these two points will be
Two bulbs of $500\, watt$ and $200\, watt$ are manufactured to operate on $220\, volt$ line. The ratio of heat produced in $500\, W$ and $200\, W$, in two cases, when firstly they are joined in parallel and secondly in series, will be
In order to quadruple the resistance of a uniform wire, a part of its length was uniformly stretched till the final length of the entire wire was $1.5$ times the original length, the part of the wire was fraction equal to