Assertion : In the purely resistive element of a series $LCR$ $AC$ circuit,the maximum value of $rms$ current increases with an increase in the angular frequency of the applied $e.m.f$.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.
Reason : $I_{\max} = \frac{\varepsilon_{\max}}{Z}$,where $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ and $I_{\max}$ is the peak current in a cycle.
- AIf both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
- BIf both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
- CIf the Assertion is correct but Reason is incorrect.
- DIf both the Assertion and Reason are incorrect.
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Similar Questions
$L$,$C$,and $R$ represent the physical quantities inductance,capacitance,and resistance,respectively. Which of the following combinations has the dimensions of frequency?
Medium
View SolutionAn $AC$ voltmeter connected between points $A$ and $B$ in the circuit below reads $36 \,V$. If it is connected between $A$ and $C$,the reading is $39 \,V$. The reading when it is connected between $B$ and $D$ is $25 \,V$. What is the reading when it is connected between $A$ and $D$? (Assume that the voltmeter reads true $rms$ voltage values and that the source generates a pure $AC$.)
DifficultKVPY 2015
View Solution$A$ circuit with an electrical load having impedance $Z$ is connected with an $AC$ source as shown in the diagram. The source voltage varies in time as $V(t) = 300 \sin (400 t) \text{ V}$,where $t$ is time in seconds. List-$I$ shows various options for the load. The possible currents $i(t)$ in the circuit as a function of time are given in List-$II$. Choose the option that describes the correct match between the entries in List-$I$ to those in List-$II$. List-$I$ List-$II$ $(P)$ Resistor $R = 30 \ \Omega$ $(1)$ $i(t) = 5 \sin(400t)$ $(Q)$ Resistor $R = 30 \ \Omega$ and Inductor $L = 100 \text{ mH}$ $(2)$ $i(t) = 6 \sin(400t + 53^{\circ})$ $(R)$ Capacitor $C = 50 \ \mu\text{F}$,Resistor $R = 30 \ \Omega$,and Inductor $L = 25 \text{ mH}$ $(3)$ $i(t) = 10 \sin(400t)$ $(S)$ Capacitor $C = 50 \ \mu\text{F}$,Resistor $R = 60 \ \Omega$,and Inductor $L = 125 \text{ mH}$ $(4)$ $i(t) = 20 \sin(400t - 90^{\circ})$ $(5)$ $i(t) = 6 \sin(400t - 53^{\circ})$
| List-$I$ | List-$II$ |
| $(P)$ Resistor $R = 30 \ \Omega$ | $(1)$ $i(t) = 5 \sin(400t)$ |
| $(Q)$ Resistor $R = 30 \ \Omega$ and Inductor $L = 100 \text{ mH}$ | $(2)$ $i(t) = 6 \sin(400t + 53^{\circ})$ |
| $(R)$ Capacitor $C = 50 \ \mu\text{F}$,Resistor $R = 30 \ \Omega$,and Inductor $L = 25 \text{ mH}$ | $(3)$ $i(t) = 10 \sin(400t)$ |
| $(S)$ Capacitor $C = 50 \ \mu\text{F}$,Resistor $R = 60 \ \Omega$,and Inductor $L = 125 \text{ mH}$ | $(4)$ $i(t) = 20 \sin(400t - 90^{\circ})$ |
| $(5)$ $i(t) = 6 \sin(400t - 53^{\circ})$ |
In the circuit shown below,what will be the readings of the voltmeter and ammeter?
Difficult
View SolutionThe following figure shows an $AC$ generator connected to a 'black box' through a pair of terminals. The box contains possible $R, L, C$ or their combination,whose elements and arrangements are not known to us. Measurements outside the box reveal that $e = 75 \sin(\omega t) \text{ V}$ and $i = 1.5 \sin(\omega t + 45^\circ) \text{ A}$. Then,the wrong statement is:
Medium
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