21.

An electrical cable having a resistance of 0.2 Ω delivers 10 kW at 200 V DC to a factory. What is the efficiency of transmission ?

• 65 %

• 75 %

• 85 %

• 95 %

A wire of resistance 5 Ω is drawn out so that its new length is 3 times its original length. What is the resistance of the new wire ?

• 45 Ω

• 15 Ω

• 5/3 Ω

• 5 Ω

Two identical cells each of emf E and internal resistance r are connected in parallel with an external resistance R. To get maximum power developed across R, the value of R is

• $\mathrm{R} = \frac{\mathrm{r}}{2}$

• R = r

• $\mathrm{R} = \frac{\mathrm{r}}{3}$

• R = 2r

An alternating current of rms value 10 A is passed through a 12 Ω resistor. The maximum potential difference across the resistor is

• 20 V

• 90 V

• 169.68 V

• None of these

Which of the following relation represents Biot-Savart's law ?

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \overrightarrow{\mathrm{r}}}}{\mathrm{r}}$

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \stackrel{\wedge }{\mathrm{r}}}}{{\mathrm{r}}^3}$

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \overrightarrow{\mathrm{r}}}}{{\mathrm{r}}^3}$

• $\overrightarrow{\mathrm{dB} } = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \frac{{\displaystyle \overrightarrow{\mathrm{dl}} \times \overrightarrow{\mathrm{r}}}}{{\mathrm{r}}^4}$

At a certain place, the horizontal component of earth's magnetic field is $\sqrt{3}$ times the vertical component. The angle of dip at that place is

• 30°

• 60°

• 45°

• 90°

The number of electron in 2 coulomb of charge is

• 5 × 10²⁹

• 12.5 × 10¹⁸

• 1.6 × 10¹⁹

• 9 × 10¹¹

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

If the charge on a capacitor is increased by 2 coulomb, the energy stored in it increases by 21 %. The original charge on the capacitor is

• 10 C

• 20 C

• 30 C

• 40 C

Four capacitors of equal capacitance have an equivalent capacitance C₁ when connected in series and an equivalent capacitance C₂ when connected in parallel. The ratio $\frac{{\mathrm{C}}_1}{{\mathrm{C}}_2}$ is

• 1/4

• 1/16

• 1/8

• 1/12