Two batteries with emf $12 \mathrm{V}$ and $13 \mathrm{V}$ are connected in parallel across a load resistor of $10 \mathrm{\Omega }$. The internal resistances of the two batteries are $1 \mathrm{\Omega }$ and $2 \mathrm{\Omega }$, respectively. The voltage across the load lies between

Consider a thin square sheet of side $L$ and thickness $t$ made of a material of resistivity $\rho .$ The resistance between two opposite faces shown by the shaded areas in the figure is

In an aluminium $\left(\mathrm{Al}\right)$ bar of a square cross-section, a square hole is drilled and is filled with iron $\left(\mathrm{Fe}\right)$ as shown in the figure. The electrical resistivity of $\mathrm{Al}$ and $\mathrm{Fe}$ are $2.7\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$ and $1.0\times {10}^{-7} \mathrm{\Omega } \mathrm{m}$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is:

For the resistance network shown in the figure, choose the correct option(s).

Two ideal batteries of emf $V_1$ and $V_2$ and three resistances $R_1$, $R_2$ and $R_3$ are connected as shown in the figure. The current in resistance $R_2$ would be zero if

In the circuit shown below, the key is pressed at time $t=0.$ Which of the following statement(s) is (are) true?

At time $t=0,$ a battery of $10 \mathrm{V}$ is connected across points $A$ and $B$ in the given circuit. If the capacitors have no charge initially, at what time (in $\mathrm{seconds}$) does the voltage across them becomes $4 \mathrm{V}$? [Take $\ln 5=1.6, \ln 3=1.1$]

In the following circuit, the current through the resistor $R\left(=2\mathrm{\Omega }\right)$ Just above Battery is $I$ Amperes. The value of $I$ is: