Q. A building is 40 m high. From a point on the ground, the angle of elevation to the top of the building is 60 degrees. What is the distance from the point to the base of the building?
A.20√3 m
B.40 m
C.30 m
D.10√3 m
Solution
Using tan(60°) = height/distance, we have distance = height/tan(60°) = 40/√3 = 20√3 m.
Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. If the frequency of the AC source is increased, what happens to the capacitive reactance?
A.Increases
B.Decreases
C.Remains the same
D.Becomes infinite
Solution
Capacitive reactance (X_C) is given by X_C = 1/(2πfC). If the frequency (f) increases, X_C decreases.
Q. A capacitor in an AC circuit has a capacitive reactance of 50 ohms. What is the frequency if the capacitance is 10 microfarads?
A.1 kHz
B.10 kHz
C.100 Hz
D.1000 Hz
Solution
Capacitive reactance (X_C) is given by X_C = 1 / (2πfC). Rearranging gives f = 1 / (2πX_CC). Substituting X_C = 50 ohms and C = 10 x 10^-6 F gives f = 318.31 Hz, approximately 1 kHz.
Q. A capacitor is charged to a voltage V and then disconnected from the battery. If the distance between the plates is doubled, what happens to the voltage across the capacitor?
A.It doubles
B.It halves
C.It remains the same
D.It quadruples
Solution
When the distance is doubled, the capacitance decreases, leading to an increase in voltage since Q = CV is constant.
Q. A capacitor is charged to a voltage V and then disconnected from the battery. If the distance between the plates is increased, what happens to the charge?
A.Increases
B.Decreases
C.Remains the same
D.Becomes zero
Solution
When a capacitor is disconnected from the battery, the charge remains constant. Increasing the distance decreases capacitance but does not affect the charge.
Q. A capacitor is charged to a voltage V and then disconnected from the battery. What happens to the charge on the capacitor if the voltage is doubled?
A.Charge doubles
B.Charge halves
C.Charge remains the same
D.Charge quadruples
Solution
The charge on a capacitor is given by Q = C * V. If the voltage is doubled, the charge also doubles, assuming capacitance remains constant.
Q. A capacitor is charged to a voltage V and then disconnected from the battery. What happens to the charge on the capacitor if the distance between the plates is increased?
A.Charge increases
B.Charge decreases
C.Charge remains the same
D.Charge becomes zero
Solution
When a capacitor is disconnected from the battery, the charge remains constant. Increasing the distance decreases capacitance but does not change the charge.
Q. A capacitor of capacitance C is charged to a voltage V and then connected in parallel with another uncharged capacitor of capacitance C. What is the final voltage across the capacitors?
A.V/2
B.V
C.2V
D.0
Solution
When connected in parallel, the total charge is conserved. The final voltage across both capacitors is V/2.
Q. A capacitor of capacitance C is charged to a voltage V and then connected to another uncharged capacitor of capacitance C. What is the final voltage across both capacitors?
A.V/2
B.V
C.2V
D.0
Solution
When connected, charge redistributes between the two capacitors, resulting in a final voltage of V/2 across each.
Q. A capacitor of capacitance C is connected to a battery of voltage V. If the battery is removed and the capacitor is connected to another capacitor of capacitance 2C, what is the final voltage across the combination?
A.V/3
B.V/2
C.V
D.2V
Solution
When the charged capacitor C is connected to an uncharged capacitor 2C, the final voltage is V_final = Q_total / C_eq = V/(1 + 1/2) = V/3.
