Physics Class 12 NCERT Solutions: Chapter 3 Current Electricity Part 2

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Series and parallel formulas

Series and Parallel Formulas

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Q: 4. (A) Three resistors and are combined in parallel. What is the total resistance of the combination?

(B) If the combination is connected to a battery of emf and negligible internal resistance, determine the current through each resistor, and the total current drawn from the battery.

Answer:

(A) There are three resistors of resistances,

They are connected in parallel. Hence, total resistance(R) of the combination is given by,

Therefore, total resistance of the combination is .

(B) Emf of the battery,

Current flowing through resistor is given by,

Current flowing through resistor is given by,

Current flowing through resistor is given by,

Total current,

Therefore, the current through each resister is , and respectively and the total current is .

Q: 5. At room temperature the resistance of a heating element is . What is the temperature of the element if the resistance is found to be , given that the temperature coefficient of the material of the resistor is?

Answer:

Room temperature,

Resistance of the heating element at

Let is the increased temperature of the filament.

Resistance of the heating element at

Temperature co-efficient of the material of the filament,

is given by the relation,

Therefore, , the resistance of the element is .

Q: 6. A negligibly small current is passed through a wire of length and uniform cross- section, and its resistance is measured to be. What is the resistivity of the material at the temperature of the experiment?

Answer:

Resistivity of material can be calculated as:

Length of the wire,

Area of cross-section of the wire,

Resistance of the material of the wire,

Resistivity of the material of the wire

Resistance is related with the resistivity as:

Therefore, the resistivity of the material is.

Q: 7. A silver wire has a resistance of at , and a resistance of at . Determine the temperature coefficient of resistivity of silver.

Answer:

Temperature,

Resistance of the silver wire at

Temperature,

Resistance of the silver wire at

Temperature coefficient of silver

It is related with temperature and resistance as

Therefore, the temperature coefficient of silver is .