When 100 , V DC is applied across a solenoid, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For $DC$,the solenoid acts as a pure resistor $R$. Given $V = 100 \, V$ and $I = 1 \, A$,the resistance is $R = \frac{V}{I} = \frac{100}{1} = 100

Vedclass · Accepted Answer

$200 \, \Omega$ and $0.55 \, H$

Vedclass · Answer

(A) For $DC$,the solenoid acts as a pure resistor $R$. Given $V = 100 \, V$ and $I = 1 \, A$,the resistance is $R = \frac{V}{I} = \frac{100}{1} = 100 \, \Omega$.For $AC$,the solenoid acts as an $LR$ circuit. Given $V = 100 \, V$ and $I = 0.5 \, A$,the impedance is $Z = \frac{V}{I} = \frac{100}{0.5} = 200 \, \Omega$.The impedance $Z$ is related to resistance $R$ and inductive reactance $X_L$ by $Z = \sqrt{R^2 + X_L^2}$.Substituting the values: $200 = \sqrt{100^2 + X_L^2} \Rightarrow 40000 = 10000 + X_L^2 \Rightarrow X_L^2 = 30000 \Rightarrow X_L = \sqrt{30000} \approx 173.2 \, \Omega$.Since $X_L = 2 \pi f L$,we have $L = \frac{X_L}{2 \pi f} = \frac{173.2}{2 	imes 3.14 	imes 50} = \frac{173.2}{314} \approx 0.55 \, H$.

When $100 \, V$ $DC$ is applied across a solenoid,a current of $1 \, A$ flows in it. When $100 \, V$ $AC$ is applied across the same coil,the current drops to $0.5 \, A$. If the frequency of the $AC$ source is $50 \, Hz$,the impedance and inductance of the solenoid are:

Similar Questions

Observe the statements given below :
Assertion $(A)$ : $f(x)=x e^{-x}$ has the maximum at $x=1$
Reason $(R)$ : $f^{\prime}(1)=0$ and $f^{\prime \prime}(1) < 0$
Which of the following is correct?

If the sum of two of the roots of $x^3+p x^2-q x+r=0$ is zero,then $p q$ is equal to

For a first order reaction,the concentration of reactant was reduced from $0.03 \ mol \ L^{-1}$ to $0.02 \ mol \ L^{-1}$ in $25 \ min$. What is its rate (in $mol \ L^{-1} \ s^{-1}$)?

$A$ particle at the end of a spring executes simple harmonic motion with a period $t_1$,while the corresponding period for another spring is $t_2$. If the period of oscillation with the two springs in series is $T$,then

The half-life of a radioactive isotope $X$ is $50 \, years$. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be ........ $years$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module