Question

An Inductance L and a resistance R are connected to a source of emf as shown in figure 30.11. When switch S1 is closed, a current begins to flow. The time required for the current to reach one-half its final value is

A. Directly proportional to RL
B. Directly proportional to R/L
C. Directly proportional to L/R
D. Directly Proportional to I/(RL)
E. Independent of L

Answer 1

The time required for the current to reach half of its final value in an RL circuit is directly proportional to L/R, following an exponential behavior. So, the best answer is c, Directly proportional to L/R.

Step-by-step explanation:

The question involves an RL circuit in which an inductance (L) and resistance (R) are connected to a source of emf.

When the switch S1 is closed, current starts flowing in the circuit, reaching half of its final steady value Io = V/R in a certain amount of time.

This process is governed by the RL circuit time constant τ = L/R, which represents the time taken for the current to reach approximately 63% of its final value.

The time required for the current to reach half of its final value in an RL circuit is given by t = (L/R)ln(2), where ln(2) is the natural logarithm of 2 and is approximately equal to 0.693.

Therefore, the time taken for the current to reach 50% of the final value is directly proportional to the ratio of the inductance to the resistance, which is L/R.

So, the best answer is c, Directly proportional to L/R.

Answer 2

The time required for the current in an RL circuit to reach one-half its final value is directly proportional to the inductance to resistance ratio, L/R.

Step-by-step explanation:

When an inductance (L) and a resistance (R) are connected to a source of emf and switch S1 is closed, the circuit behaves as an RL circuit. Initially, the inductor opposes changes in current, resulting in an exponential increase in current over time. The time constant for an RL circuit, which characterizes how quickly current reaches a certain fraction of its final value, is given by the ratio L/R. Therefore, the time required for the current to reach one-half its final value is directly proportional to the time constant of the circuit, and hence is directly proportional to L/R.