The current flowing through a wire depends on time as I = 3t² + 2t + 5. The charge flowing through the cross-section of the wire in time from t = 0 to t = 2 s is 

• 22 C

• 20 C

• 18 C

• 5 C

Two cells each of same emf e but of internal resistances r₁ and r₂ are connected in series through an external resistance R. If the potential difference between the ends of the first cell is zero, what will be the value of R in terms of r₁ and r₂ ?

The reading of the ammeter in the following figure will be

• 0.8 A

• 0.6 A

• 0.4 A

• 0.2 A

424.

A wire of resistance R is elongated n-fold to make a new uniform wire. The resistance of new wire

• nR

• n²R

• 2nR

• 2n²R

A battery of emf E and internal resistance r is connected across a pure resistive device (such as an electric heater) of resistance R. Prove that the power output of the device will be maximum if R = r.

The resistance across A and B in the figure below will be 

• 3R

• R

• $\frac{\mathrm{R}}{3}$

• None of the above

Five equal resistance, each of resistance R are connected as shown in figure below. A battery of V volt is connected between A and B. The current flowing in FC will be

• $\frac{3\mathrm{V}}{\mathrm{R}}$

• $\frac{\mathrm{V}}{\mathrm{R}}$

• $\frac{\mathrm{V}}{2\mathrm{R}}$

• $\frac{2\mathrm{V}}{\mathrm{R}}$

Two cells with the same emf E and different internal resistances r₁ and r₂ are connected in series to an  external resistance R. The value of R so that the potential difference across the first cell be zero, is

• $\sqrt{{\mathrm{r}}_1{\mathrm{r}}_2}$

• r₁ + r₂

• r₁ − r₂

• $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{2}$

What current will flow through the 2 k Ω resistor in the circuit shown in the figure ?

• 3 mA

• 6 mA

• 12 mA

• 36 mA

The I- V characteristics of a metal wire at two different temperatures (T₁ and T₂) are given in the adjoining figure. Here, we can conclude that

• T₁ > T₂

• T₁ < T₂

• T₁ = T₂

• T₁ = 2T₂