For The Circuit Shown In The Drawing, What Is The Voltage V1 Across Resistance R1?

Two wires of equal length, one of aluminium and the other of copper have the same resistance. Which of the two wires is lighter? Hence explain why aluminium wires are preferred for overhead power cables. (ρ _Al = 2.63 x 10 ^-8 Ω m, ρ _Cu = 1.72 x 10 ^–8 Ω m, Relative density of Al = 2.7, of Cu = 8.9).

$straight R space equals space straight rho straight l over straight A space equals space straight rho straight l squared over Al space equals space ρl squared over straight V space equals space fraction numerator ρl squared straight d over denominator straight m end fraction straight V space equals space straight m over straight d$
where V = volume of wire = Al
m = mass of wire
d = density of wire material
mass = volume x density = Ald
where V
It indicates that aluminium wire is lighter than copper wire. Therefore, aluminium wires are preferred in overhead cables.

Determine the equivalent resistance of networks shown in the figures (a) and (b) below.

(a) In a metre bridge, the balance point is found to be at 39.5 cm from the end A, when the resistor Y is of 12.5 Ω. Determine the resistance of X. Why are the connections between resistors in a Wheatstone or Meter bridge made of thick copper strips?
(b) Determine the balance point of the bridge above if X and Y are interchanged?
(c) What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the galvanometer show any current?

(a) Given,
Distance of jockey from end A at the balance point, l = 39.5 cm.
Standard known resistance, S = Y = 12.5 Ω
We have to determine the unknown resistance, R=X

Using the relation for balance condition we get,

S = \frac{100 - l}{l} \times R

∴

12.5 = \frac{100 - 39.5}{39.5} \times X

X = \frac{12.5 \times 39.5}{60.5} = 8.16 Ω

Thick copper strips helps to minimise resistance of the connections and hence they are used. (b) If, X and Y are interchanged,then, lengths are also interchanged.
Therefore, length modifies to , l =100 – 39.5 = 60.5 cm.

(c) If the galvanometer and cell are interchanged, the position of the balance point remains unchanged. Hence, the galvanometer will show no current.

For The Circuit Shown In The Drawing, What Is The Voltage V1 Across Resistance R1?

Source: https://www.zigya.com/study/book?class=12&board=hbse&subject=Physics&book=Physics+Part+I&chapter=Current+Electricity&q_type=&q_topic=Combination+of+Resistors+%E2%80%94+Series+and+Parallel&q_category=&question_id=PHEN12050818

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