The charge flowing through a resistance \(R\) varies with time \(t\) as \(Q=at-bt^2,\) where \(a\) and \(b\) are positive constants. The total heat produced in \(R\) is:

1.	\(\dfrac{a^3R}{3b}\)	2.	\(\dfrac{a^3R}{2b}\)
3.	\(\dfrac{a^3R}{b}\)	4.	\(\dfrac{a^3R}{6b}\)

A circuit contains an ammeter, a battery of \(30~\text{V},\) and a resistance \(40.8~\Omega\)$$ all connected in series. If the ammeter has a coil of resistance \(480~\Omega\)$$ and a shunt of \(20~\Omega,\)$$ then the reading in the ammeter will be:
1. \(0.5~\text{A}\)
2. \(0.02~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)

A potentiometer wire has a length of \(4​​~\text{m}\) and resistance  \(8~\Omega.\)  The resistance that must be connected in series with the wire and an energy source of emf \(2~\text{V}\), so as to get a potential gradient of \(1~\text{mV}\) per cm on the wire is:
1. \(32~\Omega\)
2. \(40~\Omega\)
3. \(44~\Omega\)
4. \(48~\Omega\)

\({A, B}~\text{and}~{C}\) are voltmeters of resistance \(R,\) \(1.5R\) and \(3R\) respectively as shown in the figure above. When some potential difference is applied between \({X}\) and \({Y},\) the voltmeter readings are \({V}_{A},\) \({V}_{B}\) and \({V}_{C}\) respectively. Then:

        

The figure given below shows a circuit when resistances in the two arms of the meter bridge are \(5~\Omega\) and \(R\), respectively. When the resistance \(R\) is shunted with equal resistance, the new balance point is at \(1.6l_1\). The resistance \(R\) is:

In the circuit shown cells, \(A\) and \(B\) have negligible resistance. For \(V_A =12 ~\text{V},\) \(R_1 = 500 ~\Omega ,\) and $\mathrm{}$\(R = 100 ~\Omega ,\) the galvanometer \((\text{G}) \) shows no deflection. The value of \(V_B\) is: 
     

1. \(4~\text V\) 
2. \(2~\text V\) 
3. \(12~\text V\) 
4. \(6~\text V\) 

If power dissipated in the \(9~\Omega\) resistor in the circuit shown is \(36\) W, the potential difference across the \(2~\Omega\) resistor will be: