In the circuit shown,the resistance $r$ is a variable resistance. If for $r = fR$,the heat generation in $r$ is maximum,then the value of $f$ is:

The figure shows a circuit having eight resistances of $1 \Omega$ each,labelled $R_1$ to $R_8$,and two ideal batteries with voltages $\varepsilon_1=12 V$ and $\varepsilon_2=6 V$. Which of the following statement$(s)$ is(are) correct?
$(A)$ The magnitude of current flowing through $R_1$ is $7.2 A$.
$(B)$ The magnitude of current flowing through $R_2$ is $1.2 A$.
$(C)$ The magnitude of current flowing through $R_3$ is $4.8 A$.
$(D)$ The magnitude of current flowing through $R_5$ is $2.4 A$.

If a high power heater is connected to electric mains,then the bulbs in the house become dim,because there is a

When two ends of a conductor are at different temperatures,the electromotive force generated between the two ends is known as:

The resistance of an ideal voltmeter is

$P$ and $Q$ are two identical wires of resistance $2000\, \Omega$ each, and $M$ is the midpoint of $PQ$. A voltmeter of resistance $1000\, \Omega$ is connected between $P$ and $M$. When a potential difference of $150\, V$ is applied across $PQ$, the reading of the voltmeter will be ............. $V$.