# Solutions of the Parallel Circuits Questions

## Finding of the equivalent resistance and the total current. Finding the voltage across any resistor that connected in parallel. Solutions of the questions about parallel connected circuits.

**Solution 1**

There are three of resistors connected in parallel in the circuit.

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R_{s} |

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R_{s} |

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R_{s} |

R_{s} = | 6 | |

4 |

R_{s} = 1.5 Ω

The right answer is option C.

**Solution 2**

There are three of resistors connected in parallel in the circuit.

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R_{s} |

R_{s} = | 48 | |

15 |

R_{s} = 3.2 Ω

The right answer is option B.

**Solution 3**

The equivalent resistance of the resistors connected in parallel is founds as following.

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R_{s} |

If R_{s} = 2 Ω

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2 |

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2 |

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2 |

8R_{2} = 4R_{2} + 16

4R_{2} = 16

R_{2} = 4 Ω

The right answer is option D.

**Solution 4**

If we find the value of resistor R_{2}, we can find its current.

The value of the resistor R_{2},

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R_{s} |

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3 |

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3 |

12R_{2} = 3R_{2} + 36

9R_{2} = 36

R_{2} = 4 Ω

The total current of the circuit.

I_{s} = | V | |

R_{s} |

I_{s} = | 36 | |

3 |

Is = 12 A

The current flow through resistor R_{2}.

IR_{2} = | I_{s}•R_{1} | |

R_{1} + R_{2} |

IR_{2} = | 12•12 | |

16 |

IR_{2} = 9 A

The right answer is option C.

**Solution 5 **

The circuit have four of resistor connected in parallel.

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R_{s} |

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R_{s} |

R_{s} = 1,5 Ω

The right answer is option D.

**Solution 6**

The voltage across the resistor R_{2} will be 60 V whatever the value of the resistor R_{2}.

The current flow through in resistor R_{2} is founds with equality of

I_{R2} = | V | |

R_{2} |

For I_{R2} = 5 A,

5 = | 60 | |

R_{2} |

R_{2} = 12 Ω

The right answer is option A.

**Solution 7**

If there are n resistor and the value of these resistors are equal, the equivalent resistance of the circuit can found as following.

R_{s }= | R | |

n |

The R value in this formula is value of any resistor.

For R = 108, n = 12,

R_{s} = | 108 | |

12 |

R_{s} = 9 Ω

In this case, the total current that drawn from supply source.

I_{s} = | 72 | |

9 |

I_{s }= 8 A

The right answer is option B.

**Solution 8**

The total current of a circuit is founds as below.

I_{s} = | V | |

R_{s} |

If the current drawn from supply source is 16 A and the supply voltage is 48 V.

R_{s} = | 48 | |

16 |

R_{s} = 3 Ω

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3 |

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3 |

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3 |

24R_{3} = 15R_{3} + 72

9R_{3} = 72

R_{3} = 8 Ω

The right answer is option B.

**Solution 9**

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4 |

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4 |

10R_{3} = 8R_{3} + 40

2R_{3} = 40

R_{3} = 20 Ω

The right answer is option D.

**Solution 10**

The equivalent resistance of the resistors in order for can draw current of 10 A from the circuit must be

R_{s} = | 60 | = 6 Ω |

10 |

The values of the resistor R_{2} and R_{3}. The equivalent resistance of these resistors is

R_{2,3} = | 60 | = 30Ω |

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The value of the equivalent resistance of R_{1} and R_{2,3} is

R_{1,2,3} = | 30 | =15 Ω |

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If a resistor R_{4} is connect to the circuit, the equivalent resistance must be 6 Ohm.

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6 |

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6 |

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6 |

15R_{4} = 6R_{4} + 90

9R_{4} = 90

R_{4} = 10 Ω

The value of the resistor which must be connect to the circuit is 10 Ω.

The right answer is option C

**Series Connected Resistor Questions**

**Parallel Circuits Subject Expression**

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28/10/2018

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