Assertion (A): When frequency is greater than resonance frequency in a series LCR circuit, it will be an inductive circuit.
Reason (R): Resultant Voltage Will lead the current.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
When frequency \(f > f_r\) in a series LCR circuit, the inductive reactance \(X_L\) is greater than the capacitive reactance \(X_C\). This makes the circuit inductive. In an inductive circuit, the resultant voltage leads the current. Hence, both assertion and reason are true, and the reason correctly explains the assertion.
Assertion (A): In ac supply we cannot feel any fluctuations of current in bulbs.
Reason (R): House hold ac supply has very low frequency.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Our eyes cannot detect flickers above \(10-15 \text{ Hz}\). Household AC supply (\(50/60 \text{ Hz}\)) changes too rapidly for us to perceive fluctuations in bulbs. Thus, Assertion (A) is true. However, \(50/60 \text{ Hz}\) is not considered a "very low frequency", thus Reason (R) is false.
Assertion (A): For an electric lamp connected in series with a variable capacitor and \( \text{ac} \) source, its brightness increases with increase of capacitance.
Reason (R): Capacitive reactance decreases with increase in capacitance of capacitor.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Capacitive reactance is given by \( X_C = frac{1}{omega C} \). As capacitance \( C \) increases, \( X_C \) decreases (R is true). A decrease in \( X_C \) leads to a decrease in the total circuit impedance \( Z \). With constant voltage \( V \), a lower \( Z \) results in higher current \( I = V/Z \), thus increasing the lamp's brightness (A is true). (R) correctly explains (A).
Assertion (A): In series RL circuit voltage leads the current.
Reason (R): In series \( \text{LCR} \) circuit current may lead the voltage.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
In a series \( text{RL} \) circuit, the inductive reactance \( X_L \) causes the voltage to lead the current, so (A) is true. In a series \( text{LCR} \) circuit, if \( X_C > X_L \), the circuit is capacitive, and current leads the voltage, so (R) is true. Both statements are true, but (R) is about a different circuit type and does not explain (A).