Electric circuits – problems and solutions

Electric circuits – problems and solutions

1. R1, = 6 Ω, R2 = R3 = 2 Ω, and voltage = 14 volt, determine the electric current in circuit as shown in figure below.

Known :

Resistor 1 (R1) = 6 Ω

Resistor 2 (R2) = 2 Ω

Resistor 3 (R3) = 2 Ω

Voltage (V) = 14 Volt

Wanted : Electric current (I)

Solution :

Equivalent resistor (R) :

R2 and R3 are connected in parallel. The equivalent resistor :

1/R23 = 1/R2 + 1/R3 = 1/2 + 1/2 = 2/2

R23 = 2/2 = 1 Ω

R1 and R23 are connected in series. The equivalent resistor :

R = R1 + R23 = 6 Ω + 1 Ω

R = 7 Ω

Electric current (I) :

I = V / R = 14 / 7 = 2 Ampere

2. Which one of the electric circuits as shown below has the bigger current.

Solution :

The resistance of the resistor is R and the electric voltage is V.

R1, R2 and R3 are connected in series. The equivalent resistor :

RA = R1 + R2 + R3 = R + R + R = 3R

Electric current (I) :

R1, R2 and R3 are connected in parallel. The equivalent resistor :

1/R = 1/R1 + 1/R2 + 1/R3 = 1/R + 1/R + 1/R = 3/R

RB = R/3

Electric current (I) :

R2 and R3 are connected in parallel. The equivalent resistor :

1/R23 = 1/R2 + 1/R3 = 1/R + 1/R = 2/R

R23 = R/2

R1 and R23 are connected in series. The equivalent resistor :

RC = R1 + R23 = R + R/2 = 2R/2 + R/2 = 3R/2

Electric current (I) :

R1 and R2 are connected in parallel. The equivalent resistor :

1/R12 = 1/R1 + 1/R2 = 1/R + 1/R = 2/R

R12 = R/2

R12 and R3 are connected in series. The equivalent resistor :

RD = R12 + R3 = R/2 + R = R/2 + 2R/2 = 3R/2

Electric current (I) :

3. R1 = 4 ohm, R2 = 6 ohm, R3 = 2 ohm, and V = 24 volt. What is the electric current in circuit as shown in figure below.

Known :

Resistor 1 (R1) = 4 Ohm

Resistor 2 (R2) = 6 Ohm

Resistor 3 (R3) = 2 Ohm

Voltage (V) = 24 Volt

Wanted : Electric current in circuit

Solution :

R1, R2 and R3 are connected in series. The equivalent resistor :

R = R1 + R2 + R3 = 4 + 6 + 2

R = 12 Ohm

Electric current :

I = V / R = 24 / 12 = 2 Ampere

4. Which one of the electric circuits as shown below has the bigger current.

Solution

Electric current in circuit A.

The equivalent resistor :

R1 = 3 Ω, R2 = 4 Ω, R3 = 4 Ω, V = 12 Volt

R2 and R3 are connected in parallel. The equivalent resistor :

1/R23 = 1/R2 + 1/R3 = 1/4 + 1/4 = 2/4 = 1/2

R23 = 2/1 = 2 Ω

R1 and R23 are connected in series. The equivalent resistor :

R = R1 + R23 = 3 Ω + 2 Ω = 5 Ω

Electric current (I) :

I = V / R = 12 / 5 = 2.4 Ampere

Electric current in circuit B.

The equivalent resistor :

R1 = 8 Ω, R2 = 2 Ω, R3 = 2 Ω, V = 36 Volt

R1, R2 and R3 are connected in series. The equivalent resistor :

R = R1 + R2 + R3 = 8 + 2 + 2 = 12 Ω

Electric current (I) :

I = V / R = 36 / 12 = 3 Ampere

Electric current in circuit C.

The equivalent resistor :

R1 = 4 Ω, R2 = 4 Ω, R3 = 6 Ω, V = 12 Volt

R2 and R3 are connected in parallel. The equivalent resistor :

1/R23 = 1/R2 + 1/R3 = 1/4 + 1/4 + 1/6 = 3/12 + 3/12 + 2/12 = 8/12

R23 = 12/8 = 1.5 Ω

Electric current (I) :

I = V / R = 12 / 1.5 = 8 Ampere

Electric current in circuit D.

The equivalent resistor :

R1 = 3 Ω, R2 = 3 Ω, R3 = 3 Ω, R4 = 3 Ω, R5 = 6 Ω, V = 24 Volt

R2, R3 and R4 are connected in parallel. The equivalent resistor :

1/R234 = 1/R2 + 1/R3 + 1/R4 = 1/3 + 1/3 + 1/3 = 3/3

R234 = 3/3 = 1 Ω

R1, R234 and R5 are connected in series The equivalent resistor :

R = R1 + R234 + R5 = 3 + 1 + 6 = 9 Ω

Electric current (I) :

I = V / R = 24 / 9 = 2.6 Ampere

5. According to figure as shown below, determine :

A. Total resistance

B. Electric current in circuit

C. Current I1

D. Current I2

Known :

Resistor 1 (R1) = 4 Ω

Resistor 2 (R2) = 4 Ω

Resistor 3 (R3) = 2 Ω

Resistor 4 (R4) = 3 Ω

Electric voltage (V) = 12 Volt

Solution :

A. Total resistance (R)

Resistor R2 and resistor R3 are connected in series. The equivalent resistor :

R23 = R2 + R3 = 4 Ω + 2 Ω = 6 Ω

Resistor R23 and resistor R4 are connected in parallel. The equivalent resistor :

1/R234 = 1/R23 + 1/R4 = 1/6 + 1/3 = 1/6 + 2/6 = 3/6

R234 = 6/3 = 2 Ω

Resistor R1 and resistor R234 are connected series. The equivalent resistor :

R = R1 + R234 = 4 Ω + 2 Ω = 6 Ω

The total resistance is 6 Ohm.

B. Electric current in circuit (I)

V = I R

V = electric voltage, I = electric current, R = electric resistance

Electric current :

I = V / R = 12 Volt / 6 Ohm = 2 Ampere

C. Electric current I1

Electric current in resistor R1 = electric current in circuit = 2 Ampere.

D. Current I2

Resistor R23 and resistor R4 are connected in parallel. The equivalent resistor R234 = 2 Ohm.

Electric current in resistor R234 = electric current in resistor R1 = 2 Ampere.

Voltage in resistor R234 is:

V = I R234 = (2 A)(2 Ohm) = 4 Volt

Voltage in resistor R234 = voltage in resistor R4 = voltage in resistor R23 = 4 Volt.

The equivalent resistor R23 is 6 Ohm.

Electric current in resistor R23 is :

I = V / R = 4 Volt / 6 Ohm = 2/3 Ampere

Electric current in resistor R23 = Electric current in resistor R2 = electric current in resistor R3 = 2/3 Ampere.

6. R1 = R2 = 10 Ω and R3 = R4 = 8 Ω. What is the electric current in circuit as shown in figure below ?

Known :

Resistor R1 = Resistor R2 = 10 Ω

Resistor R3 = Resistor R4 = 8 Ω

Electric voltage (V) = 12 Volt

Wanted : electric current (I)

Solution :

The equivalent resistor

Resistor R3 and resistor R4 are connected in parallel, the equivalent resistor :

1/R34 = 1/R3 + 1/R4 = 1/8 + 1/8 = 2/8

R34 = 8/2 = 4 Ω

Resistor R1, R2 and R34 are connected in series, the equivalent resistor :

R = R1 + R2 + R34 = 10 Ω + 10 Ω + 4 Ω = 24 Ω

Electric current :

I = V / R = 12 Volt / 24 Ohm = 0,5 Volt/Ohm = 0.5 Ampere

7. If the internal resistance of battery ignored, what is the electric current in the circuit shown in figure below.

Known :

Resistor R1 = 3 Ohm

Resistor R2 = 3 Ohm

Resistor R3 = 6 Ohm

Electric voltage (V) = 6 Volt

Wanted : Electric current (I)

Solution :

Equivalent resistor

Resistor R1 and R2 are connected in series. The equivalent resistor :

R12 = R1 + R2 = 3 Ohm + 3 Ohm = 6 Ohm

Resistor R12 and resistor 3 are connected in parallel. The equivalent resistor :

1/R = 1/R12 + 1/R3 = 1/6 + 1/6 = 2/6

R = 6/2 = 3 Ohm

Electric current :

I = V / R = 6 / 3 = 2 Ampere

8. What is the total electric current in circuit as shown in figure below.

Known :

Resistor R1 = 6 Ohm

Resistor R2 = 4 Ohm

Electric current (V) = 6 Volt

Internal resistance (r) = 0.6 Ohm

Wanted : Electric current

Solution :

Resistor R1 and resistor R2 are connected in parallel. The equivalent resistor :

1/RP = 1/R1 + 1/R2 = 1/6 + 1/4 = 4/24 + 6/24 = 10/24

RP = 24/10 = 2.4 Ohm

Resistor RP and internal resistance (r) are connected in series. The equivalent resistor :

R = RP + r = 2.4 Ohm + 0.6 Ohm = 3.0 Ohm

Electric current in circuit :

I = V / R = 6 Volt / 3 Ohm = 2 Ampere

1. What is an electric circuit?
• Answer: An electric circuit is a closed path or loop in which electric current can flow continuously. It typically consists of sources of voltage (like batteries), loads (like resistors, LEDs, motors), and conductors to connect them.
2. What distinguishes a series circuit from a parallel circuit?
• Answer: In a series circuit, components are connected end-to-end, so there’s a single path for current. In a parallel circuit, components are connected across common points or junctions, providing multiple paths for current.
3. How does Ohm’s Law relate voltage, current, and resistance in a circuit?
• Answer: Ohm’s Law states that the current () flowing through a conductor between two points is directly proportional to the voltage () across the two points and inversely proportional to the resistance (). It’s represented as .
4. What is the role of a switch in an electric circuit?
• Answer: A switch controls the flow of current in a circuit. When closed, it allows current to flow; when open, it interrupts or stops the current flow.
5. Why is a short circuit considered dangerous?
• Answer: In a short circuit, the resistance is very low, causing a very high current to flow. This can lead to overheating, fires, or damage to components and should be protected against with fuses or circuit breakers.
6. What is the function of a fuse or a circuit breaker in a circuit?
• Answer: Both fuses and circuit breakers are protective devices designed to interrupt a circuit if the current exceeds a predetermined safe level. While fuses “blow” or “melt”, breaking the circuit, circuit breakers “trip”, and can be reset after they interrupt the circuit.
7. How does Kirchhoff’s Current Law (KCL) describe currents at a junction in a circuit?
• Answer: Kirchhoff’s Current Law states that the sum of currents entering a junction is equal to the sum of currents leaving that junction. This is essentially a statement of the conservation of electric charge.
8. What is the difference between AC (Alternating Current) and DC (Direct Current)?
• Answer: DC refers to the unidirectional flow of electric charge, typically from a battery or a DC power supply. AC, on the other hand, is an electric charge that changes direction periodically, like what’s supplied from the power grid in many countries.
9. What does the term “ground” refer to in electrical circuits?
• Answer: “Ground” refers to a reference point in an electrical circuit from which other voltages are measured, or a common return path for electric current, or a direct physical connection to the Earth.
10. Why are capacitors used in electric circuits?
• Answer: Capacitors store and release electrical energy. They’re used in circuits for various purposes, such as filtering, smoothing voltage fluctuations, coupling and decoupling AC signals, and timing elements in oscillators.