Assertion (A): Choke coil is preferred over a resistor to adjust current in an \( \text{ac} \) circuit.
Reason (R): Power factor for inductance is zero.
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
Choke coils reduce current in \( text{ac} \) circuits with minimal power loss, as power dissipation \( P = V_{rms} I_{rms} cosphi \) is low due to the phase angle approaching \( 90^circ \) for a purely inductive component. Thus, \( cosphi approx 0 \) for an ideal inductor. So, (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): The divisions are equally marked on the scale of \( \text{ac} \) ammeter.
Reason (R): Heat produced is directly proportional to the current.
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
\( \text{ac} \) ammeters (hot wire type) measure current based on the heating effect, where heat produced is \( H \propto I^2 \). This quadratic relationship results in a non-linear scale, not equally marked. Thus (A) is false. Heat produced is proportional to the square of the current, not directly, so (R) is also 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).