Heating Effect of Current

In Circuit-$1$ and Circuit-$2$ shown in the figures, $R_1=1\mathrm{\Omega },R_2=2\mathrm{\Omega }$ and $R_3=3\mathrm{\Omega }$.
$P_1$ and $P_2$ are the power dissipations in Circuit-$1$ and Circuit-$2$ when the switches $S_1$ and $S_2$ are in open conditions, respectively.
$Q_1$ and $Q_2$ are the power dissipations in Circuit-$1$ and Circuit-$2$ when the switches $S_1$ and $S_2$ are in closed conditions, respectively.

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Which of the following statement(s) is(are) correct?

An electrical bulb rated $220 \mathrm{V},100 \mathrm{W}$, is connected in series with another bulb rated $220 \mathrm{V}$, $60 \mathrm{W}$. If the voltage across combination is $220 \mathrm{V}$, the power consumed by the $100 \mathrm{W}$ bulb will be about _____ $\mathrm{W}$.

Given below are two statements :
Statement I : A uniform wire of resistance $80 \mathrm{\Omega }$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5 \mathrm{\Omega }$.

Statement II : Two resistance $2R$ and $3R$ are connected in parallel in an electric circuit. The value of thermal energy developed in $3R$ and $2R$ will be in the ratio $3:2$.

In the light of the above statements, choose the most appropriate answer from the options given below

A direct current of $4 \mathrm{A}$ and an alternating current of peak value $4 \mathrm{A}$ flow through resistance of $3 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

A $220 \mathrm{V},50 \mathrm{Hz}$ AC source is connected to a $25 \mathrm{V},5 \mathrm{W}$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be

A resistor develops $300 \mathrm{J}$ of thermal energy in $15 \mathrm{s}$, when a current of $2 \mathrm{A}$ is passed through it. If the current increases to $3 \mathrm{A}$, the energy developed in $10 \mathrm{s}$ is _____ $\mathrm{J}$.

A conductor is made of an isotropic material (resistivity $\rho$ ) has rectangular cross-section. Horizontal dimension of the rectangle decreases linearly from $2x$ at one end to $x$ at the other end and vertical dimension increases from $y$ to $2y$ as shown in figure. Length of the conductor along the axis is equal to $l$ . A battery is connected across this conductor. Then:

Two long parallel conducting rails of zero resistance separated by a distance $L$ are joined to a cell of emf $E$ at one end. An external uniform magnetic field $B$ is applied normal to the plane and into the plane of the rails as shown in the figure. A conducting bar of mass $m$ and resistance $R$ is placed across the rails. The bar can slide freely parallel to itself always remaining perpendicular to the rails.

In the circuit shown in the figure $R=50\mathrm{\Omega },E_1=25\sqrt{3}$ volt and $E_2=25\sqrt{6}\sin \left(\omega t\right)$ volt where $\omega =100\pi s^{-1}$. The switch is closed at $t=0$0$ and remains closed for $14$ minutes, then it is opened

For the circuit show, all wires have negligible resistance, the battery has a constant internal resistance of $r=8.0\Omega$ and the two light bulbs $\left(B_1\right.$ and $\left.B_2\right)$ are identical, each with resistance $R_{bulb }$. The variable resistor is initially set $R=26.0\Omega$. The switch $S$ in the circuit now is closed. To what resistance must the variable resistor be set if bulb $B_1$ is to have the same brightness after the switch is closed as it did with the switch open?

Two uncharged thin concentric spherical conducting shells '$A$' and '$B$' of radii $R$ and $3R$ are connected through a resistance '$r$' and switch '$S$' initially opened as shown in the figure. A positive point charge '$Q$' is fixed at a distance $2R$ from the centre of the shells. At $t=0$, the switch ' $S$ ' is closed till the steady state is reached. Then choose the correct options(s)

A fuse made of lead wire has an area of cross-section $0.3{ \mathrm{mm}}^2$ on short circuiting the current in the fuse wire reaches $30 A$. How long (in milli second) after the short circuiting, Will the fuse begin to melt ?
For lead, specific heat $=0.022{\mathrm{calg}}^{-1}{\left({}^0\mathrm{C}\right)}^{-1}$, melting point $={327}^0\mathrm{C}$, density $=2 \mathrm{g}{ \mathrm{cm}}^{-3}$ and the resistivity $=22\times {10}^{-6}\Omega \mathrm{cm}$. The initial temperature of the wire is ${27}^0\mathrm{C}$ (neglect heat losses)

Two bulbs $25 \mathrm{W}-220 \mathrm{V}$ and $100 \mathrm{W}-220 \mathrm{V}$ are given. Which has higher resistance?

An electric iron of $750 \mathrm{W}$ Power is connected to a $220 \mathrm{V}$ Mains. The current drawn by the iron is nearly.

In Joules's heating law, when $R$, and $t$, are constant. If $H$, is taken along the $y$, axis and $I^2$,along $x$,axis. The graph is

Two heating wires of equal length are first connected in series and then in parallel. If the combinations are separately connected across the same time. The ratio of heat produced in the first case to that on the second is. 

Three equal resistors connected in series with a source of emf together dissipate $10 \mathrm{W}$ of power. The power dissipated by these resistors connected in parallel will be

Of the two bulbs used in a house one glows more brightly than the other. Then which of the following statements is true ?

An electric iron of $750 \mathrm{W}$ Power is connected to a $220 \mathrm{V}$ Mains. The current drawn by the iron is nearly.

Three equal resistors connected in series with a source of emf to-gather dissipate $10 \mathrm{W}$ of power. The power dissipated by these resistors connected in parallel will be