Question

1. You plan to build a toy house with a tiny light bulb inside that can be lit with 1 amp of current, for your little brother to entertain him! You have two D-size (1.5 V each) batteries and two 6-ohm resistors. How can you arrange the resistors to get the desired current?

A) resistors should be connected in parallel to each other and this combination in series with batteries

B) resistors may be connected in series with each other and also in series with batteries

C) resistors may be connected in series with this combination in parallel with batteries

D) None of the choices seem effective!

2. If the angle of incidence of a light ray passing first through air and then through a pyrex block is 40^o, and the angle of refraction is 25.9^o, what is the refractive index of pyrex?

A)1.07

B) 2.11

C)0.68

D) 1.47

3.The refractive index from air to glass is 1.5, and the refractive index from air to water is 1.33. What is the refractive index from glass into water?

A)0.44

B)1.13

C) 0.62

D)0.89

Answer 1

Let us understand the concepts behind all three parts.

(1) In the following circuit of toy house, our requirement is that the total current flow throughout the circuit is 1 amp.(Please see the image for the circuit diagram). According to Ohm's law, the electric current is the ratio of potential with resistance of the circuit ( More precisely the equivalent resistance of the circuit). In parallel combination of resistor, the net resistance of circuit we get, is 3 ohm. While two D batteries are connected in series so that net potential of circuit is 3 volts. Thus, we get a net current of 1 amp.

I = V/R = 3/3 =1 amp.

So, option(A) is correct.

(2) Using Snell's law for refraction i.e. n = sin i/ sin r ( here i is angle of incidence and r is angle of refraction), one can calculate the refractive index of the material.

n= sin 40 / sin 25.9

= 1.4716

This is the refractive index. Option (D) matches with it.

(3) This question makes a relative sense. Since a light beam travels for air to glass and from air to water, we require the refractive index for a case where light travels from glass to water. ( Please see the steps in image although option (D) matches with calculation).