Parallel Circuit Practice Problems Answers

Parallel Circuit Practice Problems Answers

### 1. What is the total resistance of two resistors connected in parallel? The total resistance of two resistors connected in parallel is given by the following formula: ``` Rt = 1/(1/R1 + 1/R2) ``` where: *

Rt

is the total resistance of the circuit *

R1

is the resistance of the first resistor *

R2

is the resistance of the second resistor For example, if two resistors with resistances of 10 ohms and 20 ohms are connected in parallel, the total resistance of the circuit would be: ``` Rt = 1/(1/10 + 1/20) = 5 ohms ``` ### 2. How does the current in a parallel circuit compare to the current in each individual resistor? The current in a parallel circuit is the same in each individual resistor. This is because the voltage across each resistor is the same, and the current is inversely proportional to the resistance. For example, if two resistors with resistances of 10 ohms and 20 ohms are connected in parallel, the current through each resistor would be: ``` I1 = V/R1 = V/10 = 0.1 A I2 = V/R2 = V/20 = 0.05 A ``` Note that the total current in the circuit is the sum of the currents through each resistor: ``` I = I1 + I2 = 0.1 A + 0.05 A = 0.15 A ``` ### 3. What is the voltage drop across each resistor in a parallel circuit? The voltage drop across each resistor in a parallel circuit is the same. This is because the current is the same in each resistor, and the voltage is directly proportional to the current. For example, if two resistors with resistances of 10 ohms and 20 ohms are connected in parallel, the voltage drop across each resistor would be: ``` V1 = I1R1 = 0.1 A * 10 ohms = 1 V V2 = I2R2 = 0.05 A * 20 ohms = 1 V ``` Note that the total voltage across the circuit is the sum of the voltages across each resistor: ``` V = V1 + V2 = 1 V + 1 V = 2 V ``` ### 4. How does the power dissipated in a parallel circuit compare to the power dissipated in each individual resistor? The power dissipated in a parallel circuit is the same in each individual resistor. This is because the current is the same in each resistor, and the power is directly proportional to the current squared. For example, if two resistors with resistances of 10 ohms and 20 ohms are connected in parallel, the power dissipated in each resistor would be: ``` P1 = I1^2R1 = (0.1 A)^2 * 10 ohms = 0.1 W P2 = I2^2R2 = (0.05 A)^2 * 20 ohms = 0.01 W ``` Note that the total power dissipated in the circuit is the sum of the powers dissipated in each resistor: ``` P = P1 + P2 = 0.1 W + 0.01 W = 0.11 W ``` ### 5. What are some applications of parallel circuits? Parallel circuits are used in a variety of applications, including: *

Electrical lighting:

The lights in a home are typically connected in parallel so that if one light burns out, the others will still work. *

Audio systems:

The speakers in an audio system are typically connected in parallel so that they can all play the same sound at the same volume. *

Computers:

The components inside a computer are typically connected in parallel so that they can all communicate with each other. *

Electric motors:

The windings in an electric motor are typically connected in parallel so that they can all produce the same amount of torque. Parallel circuits are a versatile and efficient way to connect electrical components. They are used in a wide variety of applications, and they can provide a number of benefits, including increased reliability, increased power, and increased flexibility.


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