Two wires A and B of the same material and having same length, have their cross sectional areas in the ratio 1 : 6. What would be the ratio of heat produced in these wires when same voltage is applied across each?
Download our app for free and get started
$\text{A}_\text{A}:\text{A}_\text{B}=1:6$
$\text{H}-\text{V}^2\frac{\text{t}}{\text{R}}$ and $\text{R}=\frac{\rho\text{l}}{\text{A}}$
$\text{H}_\text{A}=\frac{\text{V}^2\text{t}}{\frac{\rho\text{l}}{\text{A}_\text{A}}};\text{H}_\text{B}=\frac{\text{V}^2\text{t}}{\frac{\rho\text{l}}{\text{A}_\text{B}}}$
$=\frac{\text{H}_\text{A}}{\text{H}_\text{B}}=\frac{\text{V}^2\text{t}\times\text{A}_\text{A}}{\rho\text{l}}\times\frac{\rho\text{l}}{\text{V}^2\text{tA}_\text{H}}$
$\Rightarrow\frac{\text{H}_\text{A}}{\text{H}_\text{B}}=\frac{\text{A}_\text{A}}{\text{A}_\text{B}}=1:6$
$\text{H}-\text{V}^2\frac{\text{t}}{\text{R}}$ and $\text{R}=\frac{\rho\text{l}}{\text{A}}$
$\text{H}_\text{A}=\frac{\text{V}^2\text{t}}{\frac{\rho\text{l}}{\text{A}_\text{A}}};\text{H}_\text{B}=\frac{\text{V}^2\text{t}}{\frac{\rho\text{l}}{\text{A}_\text{B}}}$
$=\frac{\text{H}_\text{A}}{\text{H}_\text{B}}=\frac{\text{V}^2\text{t}\times\text{A}_\text{A}}{\rho\text{l}}\times\frac{\rho\text{l}}{\text{V}^2\text{tA}_\text{H}}$
$\Rightarrow\frac{\text{H}_\text{A}}{\text{H}_\text{B}}=\frac{\text{A}_\text{A}}{\text{A}_\text{B}}=1:6$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A uniform wire of resistance $100\Omega$ is melted and recast as a wire of length is double that of the original. What would be the resistance of the wire?View Solution
- 2View Solution
- Six lead-acid type of secondary cells each of emf 2.0 V and internal resistance $0.015\Omega$ are joined in series to provide a supply to a resistance of $8.5\ \Omega.$ What are the current drawn from the supply and its terminal voltage?
- A secondary cell after long use has an emf of 1.9 V and a large internal resistance of $380\ \Omega$ What maximum current can be drawn from the cell? Could the cell drive the starting motor of a car?
- 3View SolutionWrite any two factors on which internal resistance of a cell depends. The reading on a high resistance voltmeter, when a cell is connected across it, is 2.2 V. When the terminals of the cell are also connected to a resistance of 5 Ω as shown in the circuit, the voltmeter reading drops to 1.8 V. Find the internal resistance of the cell.
- 4View Solution
- Derive an expression for drift velocity of free electrons.
- How does drift velocity of electrons in a metallic conductor vary with increase in temperature? Explain.
- 5The four arms of a Wheatstone bridge $($Fig. $3.19)$ have the following resistances:View Solution
$AB =100 \Omega, BC =10 \Omega, CD =5 \Omega \text {, and } DA =60 \Omega \text {. }$
A galvanometer of $15 \Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10 V$ is maintained across $AC$. - 6View SolutionWrite the mathematical relation for the resistivity of a material in terms of relaxation time, number density and mass and charge of charge carriers in it. Explain, using this relation, why the resistivity of a metal increases and that of a semi-conductor decreases with rise in temperature.
- 7A cell of emf 'E' and internal resistance 'r' is connected across a variable load resistor R. Draw the plots of the terminal voltage V versus (i) R and (ii) the current I.View Solution
It is found that when R = 4$\Omega$, the current is 1 A and when R is increased to 9$\Omega$, the current reduces to 0.5 A. Find the values of the emf E and internal resistance r. - 8View SolutionAnswer the following:
- Why are the connections between the resistors in a meter bridge made of thick copper strips?
- Why is it generally preferred to obtain the balance point in the middle of the meter bridge wire?
- Which material is used for the meter bridge wire and why?
- 9State Kirchhoff’s rules. Use these rules to write the expressions for the currents $I_1, I_2$ and $I_3$ in the circuit diagram shown.View Solution
- 10View SolutionWhy are alloys used for making standard resistance coils?