# Quantitative Reasoning – Resistors!

PSA 2014_XI_Q12. Questions (i – iv) : Read the following passage and answer the questions that follow:

If you open up nearly any electronic device, you will see many small bead-like components with coloured stripes on them. These components are called resistors and they are used to control the amount of electrical current that flows through different circuit sections in the device. Most resistors have a central core made of a mixture of carbon and ceramic. A wire made of a material such as copper or nichrome is then wrapped around this core. Finally, the resistor is coated in enamel, leaving a wire poking out from either end of the resistor. The degree to which a resistor reduces the size of the current flowing through its branch of the circuit is called
its resistance. The resistance value is measured in ohms (written as Ω).When the resistance is increased, the current that flows through the resistor is proportionally decreased. So a resistor that has a low value of resistance allows a large amount of current to flow through it.Where two resistors are made of the same material, a long wire will have a higher resistance than a short wire of the same diameter. A very long wire will need to be wrapped around the core many more times than a short wire. This means that the resistance is also directly proportional to the number of coils. The cross-sectional area of the wire also affects the resistance. The larger the cross-section of the wire, the more easily an electric current can glow through it. In other words the resistance of the wire is inversely proportional
to the area of its cross-section.

Nichrome wire with a 1 mm diameter is coiled around a 5 cm long carbon core to form a resistor. The diameter of the core is 1 cm and the wire is coiled in such a way that the entire length of the core is covered with only one layer of wire.

(i) If the resistance of the nichrome wire is 2 per metre, the wire wrapped around the core will have a total
resistance that is closest to
1) 0.3 Ω
2 ) 3 Ω
3) 30 Ω
4) 300 Ω

(ii) Four resistors are made using carbon cores. The core of each resistor has been wrapped with copper wire, but
the wires have differing lengths and cross-sections as shown in the table below. Which pair of resistors has the same resistance ?
1) A and D
2) B and C
3) A and B
4) B and D

(iii) When resistors are connected in series, the electrical current passes through them one after another. When
they are connected in parallel, the current splits to travel through them at the same time. Which one of the diagrams below- shows ALL of the resistors in parallel with each other? (iv) Some resistors are too small to have, their value printed on them numerically.Instead, they have their resistance value coded as a series of coloured bands painted around their ends. Each colour stands for a different number or multiplier as shown in the table below:  For example, a resistor marked with brown, blue and yellow bands would have a value of (10 + 6) x 10000= 160 000 ohm.
An electrician needs to replace a resistor that is marked with violet, green and gold bands with a new resistor
that has twice the resistance value of the old one.

In order, what are the colours of the bands for the new resistor ?
1) black, yellow and gold
2) brown, green and black
3) orange, violet and green
4) brown, yellow, and black

Ans:

(i) Resistance of the nichrome wire is given as 2 Ω/metre. To find the total resistance we need to find the length of the nichrome wire that wraps the core:

Given:
Nichrome wire with a 1 mm diameter is coiled around a 5 cm long carbon core to form a resistor. Total number of coils can be given as,
T= Total length of carbon core/thickness of nichrome wire = 5×10-²/1×10-³ = 50

One coil measures “2πR” length of nichrome wire where R is the radius of carbon core. For 50 coils, total length of nichrome wire= 50 x 2πR =100πR.

1 meter of nichrome wire has resistance = 2 Ω
100πR meter of nichrome wire has resistance = 200πR = 200x π x 0.5 x10-2 = π ≈ 3 Ω. Option (2).

(ii) Resistance is directly proportional to length ‘L’ and inversely proportional to cross-sectional area ‘A’.

R∝ L/A

RA/RB = LA/LB * AB/AA

RA/RB = (10/20) * (4/2)= 1.

RA=RB.  Option (3)

(iii) Option 4 is correct. All other options have some resistors in series.

(iv)  Resistor marked with violet, green and gold bands has resistance = (70 + 5) x 0.1 = 7.5 ohm.

We are looking for resistor with resistance = 7.5×2 = 15 ohm.

(1) Resistor marked with black, yellow and gold bands has resistance = (0 + 4) x 10,000 = 40,000 ohm.
(2) Resistor marked with brown, green and black bands has resistance = (10 + 5) x 1 = 15 ohm.
(3) Resistor marked with orange, violet and green bands has resistance = (30 + 7) x 100,000 = 37,00,000 ohm.
(4) Resistor marked with brown, yellow and black bands has resistance = (10 + 4) x 1= 14 ohm.

Option (2). 