Two wires of the same metal have the same len | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The resistance of a wire is given by the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-

Vedclass · Accepted Answer

$40\, \Omega$

Vedclass · Answer

(D) The resistance of a wire is given by the formula $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area.Since both wires are of the same metal, $\rho$ is constant. Given that $L$ is also the same, we have $R \propto \frac{1}{A}$.Let $A_1$ be the area of the thicker wire and $A_2$ be the area of the thinner wire. Given $A_1 : A_2 = 3 : 1$, so $A_1 = 3A$ and $A_2 = A$.The resistance of the thicker wire $(R_1)$ is $10\, \Omega$. Since $R_1 = \frac{\rho L}{3A} = 10\, \Omega$, then $\frac{\rho L}{A} = 30\, \Omega$.The resistance of the thinner wire $(R_2)$ is $R_2 = \frac{\rho L}{A} = 30\, \Omega$.When joined in series, the total resistance $R_{total} = R_1 + R_2 = 10\, \Omega + 30\, \Omega = 40\, \Omega$.

Two wires of the same metal have the same length, but cross-sections are in the ratio $3 : 1$. They are joined in series. The resistance of the thicker wire is $10\, \Omega$. The total resistance of the combination will be:

Similar Questions

What is the $SI$ unit of electric charge?

If $1 \text{ ampere}$ electric current passes through a conductor,how many electrons will pass per second?

When an electric iron is connected to a $220\;V$ line and a current of $5\;A$ flows through it,what is the power of the iron?

State a difference between the wire used in the element of an electric heater and in a fuse wire.

Three $2\,\Omega$ resistors,$A$,$B$,and $C$,are connected as shown in the figure. Each of them dissipates energy and can withstand a maximum power of $18\,W$ without melting. Find the maximum current (in $A$) that can flow through the circuit such that none of the resistors melt.

Vedclass Test Series

Exam Paper Generator

Online Exam Module