In the circuit shown, the ammeter reading is zero. What is the resistance of resistor R?

Question 27

In the circuit shown, the ammeter reading is zero.

What is the resistance of resistor R?

A 100 Ω                       B 200 Ω                       C 400 Ω                       D 600 Ω

Reference: Past Exam Paper – November 2018 Paper 13 Q37

Solution:

Answer: C.

Let the negative terminals of the cells be at 0 V and the upper terminals of the cells to at their respective e.m.f.s.

For the ammeter reading to be zero, the potential difference between the 2 terminals of the ammeter should be zero. That is, both terminals of the ammeter should be at the same potential.

Note that the lower junction being at 0 V is just an assumption here and may not always be true, especially since we have 2 different cells of different e.m.f.s. In this case, the potentials at the middle junctions should also be zero for the ammeter reading to be zero. That is, there should be no potential difference between the 2 middle junctions.

Consider the left section.

We can use the potential divider equation to determine the p.d. across the resistors.

p.d. across 100 Ω = [100 / (100+50)] × 12 = 8 V

Since the lower junction is at 0 V, the middle junction on the left will be at 8 V.

For the ammeter reading to be zero, the potential at the middle junction on the right should also be at 8 V.

Consider the right section.

p.d. across the 200 Ω = 8 V

p.d. across the 200 Ω = [200 / (200+R)] × 24

[200 / (200+R)] × 24 = 8

200 × 24 = 8 × (200+R)

200 + R = (200×24) / 8

200 + R = 600

R = 600 – 200 = 400 Ω

 

Many would choose answer A, which assumes the same ratio across each pair of resistors that are facing each other in the two circuits. This is not correct because the two cells have different e.m.f.s.

An object accelerates in a direction that is always perpendicular to its motion.

Question 16

An object accelerates in a direction that is always perpendicular to its motion.

What is the effect, if any, of the acceleration on the object’s speed and direction?

speed             direction

A          changes          changes

B          changes          constant

C         constant          changes

D         constant          constant

Reference: Past Exam Paper – June 2008 Paper 1 Q6

Solution:

Answer: C.

When the acceleration is in the direction of the motion, the speed increases.

When the acceleration is in the opposite direction of the motion, the speed decreases.

When the acceleration is perpendicular to the direction of motion, the direction changes but the speed remains constant. e.g. in circular motion

 
The speed does not change because the acceleration does not have a component along the direction of motion (since it is perpendicular).

A driver stops his car in time t by gradually increasing the total braking force on the car.

Question 23

A driver stops his car in time t by gradually increasing the total braking force on the car. The graph shows the resultant force on the car.

 

Which graph shows how the speed of the car will vary during this time?

Reference: Past Exam Paper – June 2017 Paper 13 Q7

Solution:

Answer: D.

The total braking force on the car increases with time.

F = ma

So, the deceleration of the car increases with time. This means that the speed decreases at an increasing rate.

From a speed-time graph, the deceleration can be obtained by the gradient. Deceleration is indicated by a negative gradient.

I

n this case, the gradient is negative and increases with time.

D is the only graph where the gradient keeps on increasing with time.