Let's analyze and verify each statement step-by-step to determine the correct answer.
### Statement (A): Nichrome and copper wires of same length and same radius are connected in series, then the nichrome wire gets heated first.
#### Explanation:
1. Resistivity of nichrome vs. copper: Nichrome has a significantly higher resistivity compared to copper. This means that for wires of the same length and radius, the resistance of a nichrome wire will be greater than that of a copper wire.
2. Heat Generation in Series Circuits: The heat generated in a resistor can be given by the power dissipation formula [tex]\( P = I^2 R \)[/tex], where [tex]\( I \)[/tex] is the current and [tex]\( R \)[/tex] is the resistance.
3. Current in Series Circuit: When two wires are connected in series, the current passing through them is the same.
4. Implication on Heating: Given the same current, the wire with the higher resistance (in this case, the nichrome wire) will dissipate more power and, therefore, produce more heat.
Conclusion: Nichrome wire will get heated first because it has a higher resistivity which leads to higher resistance and thus higher power dissipation.
Thus, statement (A) is true.
### Statement (B): In series combination larger resistance consumes more energy
#### Explanation:
1. Energy Consumption in Series Circuit: In a series circuit, the total energy consumed over a period of time is the sum of the energies consumed by each component.
2. Power and Resistance: Using [tex]\( P = I^2 R \)[/tex], we know that for a given current [tex]\( I \)[/tex], the component with the larger resistance [tex]\( R \)[/tex] will have higher power consumption [tex]\( P \)[/tex].
3. Implication on Energy: Over time, this translates to more energy being consumed by the larger resistance, because [tex]\( E = P \times t \)[/tex], where [tex]\( t \)[/tex] is time over which the power is dissipated.
Conclusion: The larger resistance in the series combination will indeed consume more energy.
Thus, statement (B) is true.
### Final Answer:
Both statements (A) and (B) have been analyzed and found to be true. Therefore, the correct option is:
c) Both A and B are true
