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

The four arms of a Wheatstone bridge (Figure) have the following resistances: $AB = 100 \; \Omega$,$BC = 10 \; \Omega$,$CD = 5 \; \Omega$,and $DA = 60 \; \Omega$. $A$ galvanometer of $15 \; \Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10 \; V$ is maintained across $AC$.

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 ..................... $A$.

What are the uses of a Wheatstone bridge?

Consider the following two statements.
$(A)$ Kirchhoff's junction law follows from the conservation of charge.
$(B)$ Kirchhoff's loop law follows from the conservation of energy.
Which of the following is correct?

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:
$(A)$ $V_1=V_2$ and $R_1=R_2=R_3$
$(B)$ $V_1=V_2$ and $R_1=2R_2=R_3$
$(C)$ $V_1=2V_2$ and $2R_1=2R_2=R_3$
$(D)$ $2V_1=V_2$ and $2R_1=R_2=R_3$