When a current of $2 \ A$ flows through a conductor,$80 \ J$ of heat is produced in $10 \ s$. The resistance of the conductor is ........... $\Omega$.

The current in a simple series circuit is $5.0 \, A$. When an additional resistance of $2.0 \, \Omega$ is inserted, the current drops to $4.0 \, A$. The original resistance of the circuit in $\Omega$ was:

In the given circuit diagram,in the steady state,the current through the battery and the charge on the capacitor respectively are:

$A$ $dc$ source of $emf \, E_1 = 100 \, V$ and internal resistance $r = 0.5 \, \Omega$,a storage battery of $emf \, E_2 = 90 \, V$,and an external resistance $R$ are connected as shown in the figure. For what value of $R$ will no current pass through the battery $E_2$ (in $.5$)? ................ $\Omega$

Under what condition can the current passing through the resistance $R$ be increased by short-circuiting the battery of emf $E_2$? The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.

What is the equivalent resistance between $A$ and $B$ in the figure below if $R = 3\,\Omega$?