## Parallel Circuit Problems Episode 904 Answer Key

### Problem 1

In the circuit shown below, what is the total current flowing through the circuit? ``` 10 Ω / \ / \ +--+-----------+--+ +--+ | | | | | | 12 V 10 Ω 10 Ω 10 Ω | | | | | | \ / +--+ ```### Solution:

The total current flowing through the circuit is 2 A. To solve this problem, we can use the following formula: ``` I = \frac{V}{R} ``` where: *### I

is the current in amps *### V

is the voltage in volts *### R

is the resistance in ohms In this problem, we have: *### V

= 12 V *### R

= 10 Ω + 10 Ω + 10 Ω = 30 Ω So, the total current flowing through the circuit is: ``` I = \frac{12 V}{30 Ω} = 2 A ```### Problem 2

What is the voltage drop across each resistor in the circuit shown in problem 1?### Solution:

The voltage drop across each resistor is 4 V. To solve this problem, we can use the following formula: ``` V = IR ``` where: *### V

is the voltage in volts *### I

is the current in amps *### R

is the resistance in ohms In this problem, we have: *### V

= 4 V *### I

= 2 A *### R

= 10 Ω So, the voltage drop across each resistor is: ``` V = IR = 2 A * 10 Ω = 4 V ```### Problem 3

What is the power dissipated by each resistor in the circuit shown in problem 1?### Solution:

The power dissipated by each resistor is 8 W. To solve this problem, we can use the following formula: ``` P = IV ``` where: *### P

is the power in watts *### I

is the current in amps *### V

is the voltage in volts In this problem, we have: *### P

= 8 W *### I

= 2 A *### V

= 4 V So, the power dissipated by each resistor is: ``` P = IV = 2 A * 4 V = 8 W ```### Problem 4

If the resistance of each resistor in the circuit shown in problem 1 is increased by 20%, what will be the total current flowing through the circuit?### Solution:

The total current flowing through the circuit will decrease by 10%. To solve this problem, we can use the following formula: ``` I = \frac{V}{R} ``` where: *### I

is the current in amps *### V

is the voltage in volts *### R

is the resistance in ohms In this problem, we have: *### V

= 12 V *### R

= 10 Ω + 10 Ω + 10 Ω = 30 Ω So, the total current flowing through the circuit is: ``` I = \frac{12 V}{30 Ω} = 2 A ``` If the resistance of each resistor is increased by 20%, the total resistance of the circuit will increase to: ``` R = 30 Ω * 1.2 = 36 Ω ``` So, the total current flowing through the circuit will decrease to: ``` I = \frac{12 V}{36 Ω} = \frac{2}{3} A = 0.67 A ``` Therefore, the total current flowing through the circuit will decrease by 10%.### Problem 5

If the voltage in the circuit shown in problem 1 is increased by 20%, what will be the voltage drop across each resistor?Altering The Course Of Schizophrenia Progress And Perspectives Nature Reviews Discovery

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