KCET · Physics · Current Electricity
Masses of three wires of copper are in the ratio of \(1: 3: 5\) and their lengths are in the ratio of \(5: 3: 1\). The ratio of their electrical resistances is
- A \(1: 3: 5\)
- B \(5: 3: 1\)
- C \(1: 15: 125\)
- D \(125: 15: 1\)
Answer & Solution
Correct Answer
(D) \(125: 15: 1\)
Step-by-step Solution
Detailed explanation
Given, \(\quad m_{1}: m_{2}: m_{3}=1: 3: 5\)
and \(\quad I_{1}: I_{2}: I_{3}=5: 3: 1\)
We know that, electrical resistance,
\(R=\rho \frac{l}{A}\)
and \(d=\frac{m}{V}=\frac{m}{A l}\)
or \(A=\frac{m}{d l}\)
\(\Rightarrow A \propto \frac{m}{l}\)
(\(\because\) density is same for the three wires)
\(\therefore R_{1}: R_{2}: R_{3}=\frac{l_{1}}{A_{1}}: \frac{I_{2}}{A_{2}}: \frac{I_{3}}{A_{3}}\)
or \(R_{1}: R_{2}: R_{3}=\frac{l_{1}^{2}}{m_{1}}: \frac{l_{2}^{2}}{m_{2}}: \frac{l_{3}^{2}}{m_{3}}\)
\(=\frac{25}{1}: \frac{9}{3}: \frac{1}{5}\)
\(\Rightarrow R_{1}: R_{2}: R_{3}=125: 15: 1\)
and \(\quad I_{1}: I_{2}: I_{3}=5: 3: 1\)
We know that, electrical resistance,
\(R=\rho \frac{l}{A}\)
and \(d=\frac{m}{V}=\frac{m}{A l}\)
or \(A=\frac{m}{d l}\)
\(\Rightarrow A \propto \frac{m}{l}\)
(\(\because\) density is same for the three wires)
\(\therefore R_{1}: R_{2}: R_{3}=\frac{l_{1}}{A_{1}}: \frac{I_{2}}{A_{2}}: \frac{I_{3}}{A_{3}}\)
or \(R_{1}: R_{2}: R_{3}=\frac{l_{1}^{2}}{m_{1}}: \frac{l_{2}^{2}}{m_{2}}: \frac{l_{3}^{2}}{m_{3}}\)
\(=\frac{25}{1}: \frac{9}{3}: \frac{1}{5}\)
\(\Rightarrow R_{1}: R_{2}: R_{3}=125: 15: 1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- The time required for the light to pass through a glass slab (refractive index \(=1.5\) ) of thickness \(4 \mathrm{~mm}\) is
( \(c=3 \times 10^{8} \mathrm{~ms}^{-1}\), speed of light in free space)KCET 2011 Medium - A gas is taken from state A to state B along two different paths 1 and 2. The heat absorbed and work done by the system along these two paths are \(\mathrm{Q}_1\) and \(\mathrm{Q}_2\) and \(\mathrm{W}_1\) and \(\mathrm{W}_2\) respectively. ThenKCET 2025 Easy
- When the angle of incidence is \(60^{\circ}\) on the surface of a glass slab, it is found that the reflected ray is completely polarised. The velocity of light in glass isKCET 2007 Medium
- Two monochromatic light waves of amplitudes \(3 \mathrm{~A}\) and \(2 \mathrm{~A}\) interfering at a point have a phase difference of \(60^{\circ}\). The intensity at that point will be proportional toKCET 2011 Medium
- A point charge \(A\) of \(+10 \mu \mathrm{C}\) and another point charge \(B\) of \(+20 \mu \mathrm{C}\) are kept 1 m apart in free space. The electrostatic force on \(A\) due to \(B\) is \(\mathbf{F}_1\) and the electrostatic force on \(B\) due to \(A\) is \(\mathbf{F}_2\). ThenKCET 2024 Medium
- The component of a vector \( \vec{r} \) along \( x \) - axis will have a maximum value ifKCET 2016 Easy
More PYQs from KCET
- Meera visits only one of the two temples A and B in her locality. Probability that she visits temple A is \(\frac{2}{5}\). If she visits temple \(A, \frac{1}{3}\) is the probability that she meets her friend, whereas it is \(\frac{2}{7}\) if she visits temple \(B\). Meera met her friend at one of the two temples. The probability that she met her at temple B isKCET 2025 Medium
- The line joining \(A(2,-7)\) and \(B(6,5)\) is divided into 4 equal parts by the points \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\) such that \(\mathrm{AQ}=\mathrm{RP}=\mathrm{QB}\). The mid point of \(P R\) isKCET 2010 Easy
- On the set of all natural numbers \(N\), which one of the following * is a binary operation?KCET 2009 Easy
- Compare the statements A and B.
Statement A: Blood sugar level falls rapidly after hepatectomy.
Statement B: The glycogen of the liver is the principle source of blood sugar.
Select the correct description:KCET 2009 Easy - Which of the following statements is correct with reference to vacuoles?KCET 2024 Medium
- The negation of \(p \rightarrow(\sim p \vee q)\) isKCET 2011 Hard