Q. A circle has an area of 78.5 cm². What is the radius? (Use π = 3.14) (2022)
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A.
5 cm
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B.
7 cm
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C.
10 cm
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D.
12 cm
Solution
Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.
Correct Answer: B — 7 cm
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Q. A circle is defined by the equation x² + y² - 10x + 6y + 25 = 0. What is the radius of the circle?
Solution
Rearranging gives (x - 5)² + (y + 3)² = 9, so the radius is √9 = 3.
Correct Answer: A — 5
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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)
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A.
78.5 cm²
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B.
100 cm²
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C.
50 cm²
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D.
25 cm²
Solution
Radius = 10/2 = 5 cm; Area = πr² = π * 5² = 78.5 cm².
Correct Answer: A — 78.5 cm²
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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (Use π = 3.14) (2020)
-
A.
78.5 cm²
-
B.
50 cm²
-
C.
100 cm²
-
D.
25 cm²
Solution
Radius of the circle = side/2 = 10 cm / 2 = 5 cm. Area = πr² = 3.14 * 5² = 78.5 cm².
Correct Answer: A — 78.5 cm²
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Q. A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)
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A.
50.24 cm²
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B.
64 cm²
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C.
25.12 cm²
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D.
32 cm²
Solution
Radius = 8/2 = 4 cm; Area = πr² = π * 4² = 50.24 cm².
Correct Answer: A — 50.24 cm²
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Q. A circle is inscribed in a triangle with sides 7, 8, and 9. What is the radius of the circle?
Solution
Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.
Correct Answer: B — 5
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Q. A circle is inscribed in a triangle with sides 7, 8, and 9. What is the radius of the inscribed circle?
Solution
Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.
Correct Answer: B — 4
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Q. A circle is tangent to the x-axis at the point (4, 0). What is the equation of the circle if its radius is 3?
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A.
(x - 4)² + (y - 3)² = 9
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B.
(x - 4)² + (y + 3)² = 9
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C.
(x + 4)² + (y - 3)² = 9
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D.
(x + 4)² + (y + 3)² = 9
Solution
The center of the circle is (4, 3) since it is 3 units above the tangent point (4, 0).
Correct Answer: B — (x - 4)² + (y + 3)² = 9
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Q. A circle passes through the points (1, 2), (3, 4), and (5, 6). What is the radius of the circle?
Solution
Using the distance formula, the radius can be calculated from the center found using the circumcircle method.
Correct Answer: B — 3
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Q. A circuit consists of a 9V battery and two resistors of 3Ω and 6Ω in series. What is the current flowing through the circuit? (2021)
Solution
Total resistance R = 3Ω + 6Ω = 9Ω. Current I = V/R = 9V / 9Ω = 1A.
Correct Answer: B — 2A
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Q. A circuit contains a 10Ω resistor and a 5Ω resistor in series with a 15V battery. What is the total current in the circuit?
Solution
Total resistance R = 10Ω + 5Ω = 15Ω. Current I = V/R = 15V/15Ω = 1A.
Correct Answer: B — 2A
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Q. A circuit contains a 10Ω resistor and a 5Ω resistor in series. What is the total resistance?
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A.
5Ω
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B.
10Ω
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C.
15Ω
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D.
50Ω
Solution
In series, total resistance R = R1 + R2 = 10Ω + 5Ω = 15Ω.
Correct Answer: C — 15Ω
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Q. A circuit contains a 12 V battery and two resistors of 4 ohms and 8 ohms in series. What is the current flowing through the circuit?
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A.
0.5 A
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B.
1 A
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C.
1.5 A
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D.
2 A
Solution
Total resistance R = 4 + 8 = 12 ohms. Current I = V/R = 12 V / 12 ohms = 1 A.
Correct Answer: B — 1 A
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Q. A circuit contains a 12V battery and two resistors of 4 ohms and 8 ohms in series. What is the total current in the circuit?
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A.
1 A
-
B.
0.5 A
-
C.
2 A
-
D.
3 A
Solution
Total resistance R = R1 + R2 = 4 + 8 = 12 ohms. Current I = V/R = 12V / 12 ohms = 1 A.
Correct Answer: B — 0.5 A
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Q. A circuit contains a 12V battery and two resistors of 4Ω and 6Ω in parallel. What is the total current supplied by the battery? (2019)
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A.
1.2 A
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B.
2 A
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C.
3 A
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D.
4 A
Solution
First, find the equivalent resistance R_eq = 1/(1/4 + 1/6) = 2.4Ω. Then, I = V/R_eq = 12V/2.4Ω = 5 A.
Correct Answer: C — 3 A
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Q. A circuit contains a 9V battery and two resistors in series: 3Ω and 6Ω. What is the voltage across the 6Ω resistor?
Solution
The total resistance R_total = 3Ω + 6Ω = 9Ω. The current I = V/R_total = 9V / 9Ω = 1A. Voltage across 6Ω, V = I * R = 1A * 6Ω = 6V.
Correct Answer: A — 6V
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Q. A circuit contains a 9V battery and two resistors of 3 ohms and 6 ohms in series. What is the voltage drop across the 6 ohm resistor?
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A.
3 V
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B.
6 V
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C.
9 V
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D.
4.5 V
Solution
Total resistance R_total = 3 + 6 = 9 ohms. Current I = V/R_total = 9V / 9Ω = 1 A. Voltage drop across 6 ohm resistor = I * R = 1 A * 6Ω = 6 V.
Correct Answer: B — 6 V
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Q. A circuit contains a 9V battery and two resistors of 3 ohms and 6 ohms in series. What is the voltage across the 6 ohm resistor?
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A.
6V
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B.
3V
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C.
9V
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D.
4.5V
Solution
Total resistance R_total = 3 + 6 = 9 ohms. Current I = V/R_total = 9V / 9Ω = 1 A. Voltage across 6 ohm resistor = I * R = 1 A * 6Ω = 6V.
Correct Answer: A — 6V
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Q. A circuit contains a 9V battery and two resistors of 3Ω and 6Ω in series. What is the voltage across the 6Ω resistor?
Solution
The total resistance R_total = 3Ω + 6Ω = 9Ω. The current I = V/R_total = 9V / 9Ω = 1A. Voltage across 6Ω, V = I * R = 1A * 6Ω = 6V.
Correct Answer: A — 6V
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Q. A circuit has a 15V battery and a 5Ω resistor. What is the voltage drop across the resistor? (2021)
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A.
3V
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B.
5V
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C.
15V
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D.
10V
Solution
The voltage drop across the resistor is equal to the battery voltage, which is 15V.
Correct Answer: C — 15V
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Q. A circuit has a 15V battery and a total resistance of 5Ω. What is the total current flowing through the circuit? (2023)
Solution
Using Ohm's law, I = V/R = 15V/5Ω = 3A.
Correct Answer: C — 3A
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Q. A circuit has a 24V battery and a total resistance of 12Ω. What is the current flowing through the circuit? (2020)
Solution
Using Ohm's law, I = V/R = 24V / 12Ω = 2A.
Correct Answer: B — 4A
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Q. A circuit has a 9V battery and a 3Ω resistor. What is the voltage drop across the resistor? (2022)
Solution
The voltage drop across the resistor is equal to the battery voltage in a simple circuit: 9V.
Correct Answer: C — 9V
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Q. A circuit has a 9V battery and two resistors of 3Ω and 6Ω in series. What is the current flowing through the circuit? (2022)
Solution
Total resistance R = 3Ω + 6Ω = 9Ω. Current I = V/R = 9V / 9Ω = 1A.
Correct Answer: B — 2A
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Q. A circuit has a current of 2A and a resistance of 6Ω. What is the voltage across the circuit? (2020)
-
A.
6V
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B.
12V
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C.
8V
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D.
10V
Solution
Using Ohm's Law, V = I * R = 2A * 6Ω = 12V.
Correct Answer: B — 12V
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Q. A circuit has a current of 3A and a resistance of 6Ω. What is the voltage across the circuit? (2019)
Solution
Using Ohm's Law, V = I * R = 3A * 6Ω = 18V.
Correct Answer: A — 9V
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Q. A circuit has a current of 5A and a resistance of 10Ω. What is the power consumed in the circuit? (2020)
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A.
25W
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B.
50W
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C.
75W
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D.
100W
Solution
Power (P) can be calculated using P = I^2 * R = (5A)^2 * 10Ω = 25 * 10 = 250W.
Correct Answer: B — 50W
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Q. A circuit has a current of 5A and a resistance of 2Ω. What is the power consumed in the circuit? (2020)
-
A.
10W
-
B.
25W
-
C.
50W
-
D.
100W
Solution
Power (P) can be calculated using the formula P = I^2 * R = (5A)^2 * 2Ω = 25W.
Correct Answer: B — 25W
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Q. A circuit has a resistance of 10 Ω and a reactance of 10 Ω. What is the impedance of the circuit? (2020)
-
A.
10 Ω
-
B.
14.14 Ω
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C.
20 Ω
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D.
5 Ω
Solution
The impedance Z = √(R² + X²) = √(10² + 10²) = √200 = 14.14 Ω.
Correct Answer: B — 14.14 Ω
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Q. A circuit has a resistance of 10Ω and a reactance of 5Ω. What is the impedance of the circuit? (2021)
-
A.
5Ω
-
B.
10Ω
-
C.
√125Ω
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D.
√(10² + 5²)Ω
Solution
The impedance Z is calculated as Z = √(R² + X²) = √(10² + 5²) = √125Ω.
Correct Answer: D — √(10² + 5²)Ω
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