A cylindrical wire having 10 Ω resistance is stretched to increase its length by 10 % . Calculate its new resistance.

Let the initial length of the wire be l , and the new length be l ' . Now, the increase in length is 10 % , So, l ' = l + 10 100 × l = 11 10 l Now, let the initial area of wire be A , the area after the wire is stretched be A ' , the initial resistance be R , and new resistance after the wire is stretched be R ' . As we know that the resistance in terms of resistivity, length and area is given by the expression R = ρ L A . The volume of the wire will remain constant as l A = l ' A ' or, A ' = l A l ' Now, using the above expression R R ' = l A ' l ' A , Now,substituting the value of A ' in above equation R R ' = l 2 l ' 2 = 100 121 R ' = 121 100 R Now, the value of R = 10 Ω , The value of new resistance R ' = 121 100 × 10 = 12 . 1 Ω . Now, the percentage change in resistance = 12 . 1 - 10 10 × 100 = 21 % . Hence, the new resistance is 12 . 1 Ω .

Derive the expression to find the unknown resistance in the balance condition of wheatstone bridge

In wheatstone ' s bridge, four resistances are joined to form a parallelogram. In one diagonal of this parallelogram a galvanometer is attached, and in other diagonal, a cell. The values of resistances are so adjusted that no current flows through the galvanometer. This condition of bridge is called balanced wheatstone ' s bridge condition. Let P , Q , R and S resistances forms a bridge. Let a current, I flows through the circuit. Applying Kirchhoff ' s second law to closed loop ABDA , I 1 P - I 2 R = 0 or I 1 P = I 2 R ‐ equation 1 Applying Kirchhoff ' s second law to closed loop BCDB I 1 Q - I 2 S = 0 or I 1 Q = I 2 S ‐ equation 2 Dividing equation 1 by equation 2 , we get I 1 P I 1 Q = I 2 R I 2 S ⇒ P Q = R S This is the balanced wheatstone bridge condition. If R is the unknown resistance, P and Q are the ratio arm of the bridge and S is the standard arm, then R = P Q × S .

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 3 - Current Electricity>Gujarat Board-2020>Q 22

HARD

12th Gujarat Board

IMPORTANT

Earn 100

Determine the current in each branch of the given network.

Important Questions on Current Electricity

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 3 - Current Electricity>Gujarat Board-2018>Q 1

In potentiometer circuit shown in the figure, the balance length $AJ = 60 cm$ when the switch $S$ is open. When switch $S$ is closed, the value of $R = 3 Ω$ , the balance length $AJ' = 40 cm$ . The internal resistance of the cell is _____________.

Question Image

EASY

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 3 - Current Electricity>Gujarat Board-2018>Q 2

A student is asked to connect four cells of emf $ε$ each and internal resistance $r$ in a series helping conditions. By mistake, he connects one cell in the opposite way. What will be the effective emf and effective internal resistance :

MEDIUM

12th Gujarat Board

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 3 - Current Electricity>Gujarat Board-2018>Q 3

In a hydrogen atom, the electron is moving in a circular orbit of the radius