Assertion (A): An electric lamp is connected in series with a long solenoid of copper with air core and then connected to \( \text{ac} \) source. If an iron rod is inserted in solenoid, the lamp will become dim.
Reason (R): If an iron rod is inserted in solenoid, the inductance of solenoid increases.
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
Inserting an iron rod (ferromagnetic material) into a solenoid significantly increases its inductance \( L \) (R is true). In an \( \text{ac} \) circuit, this increases inductive reactance \( X_L =\omega L \), which in turn increases the total impedance \( Z \) of the circuit. Higher \( Z \) leads to lower current \( I = V/Z \), making the lamp dim (A is true). (R) provides the correct explanation for (A).
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).