A wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to the current, the temperature of the wire is raised by $\Delta T$ in a time $t$. A number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $4\,L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time. The value of $N$ is
- 4
- 6
- 8
- 9
The Correct Option is B
Solution and Explanation
$\, \, \, \, \, \, \, \, \bigg[ H=\frac{V^2}{R}t \bigg]$
When length of the wire is doubled, resistance and mass both are doubled.
Therefore, in the second case.
$\frac{(NE)^2}{2R} . t = (2m)s \Delta T \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, ...(ii)$
Dividing E (ii) by (i), we get
$\frac{N^2}{18} = 2 \, or \, N^2 = 36 \, or \, N = 6$
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Concepts Used:
Current Electricity
Current electricity is defined as the flow of electrons from one section of the circuit to another.
Types of Current Electricity
There are two types of current electricity as follows:
Direct Current
The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.
Alternating Current
The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.