# Solutions of The Electric Power Test-1 Questions

## Concept of power in electric circuits. Calculating power in any resistor. Finding total power drawn from supply source. Explanatory solutions of the test-1 questions.

**Solution 1**

First let we find the equivalent resistance, then let we find the main current of the circuit using the equivalent resistance that we found it.

If we find the main current, we can find current flowing through each resistors.

The power in the R_{5} is P_{5}.

P_{5} = (I_{5})^{2}*R_{5}

P_{5} = (I_{5})^{2}*6

The power in the R_{2} is P_{2}.

P_{2} = (I_{2})^{2}*R_{2}

P_{2} = (I_{2})^{2}*5

The equivalent resistance of the circuit.

R_{2,3} = 5 + 3

R_{2,3} = 8 Ω

The R_{2,3} and R_{4} are parallel.

R_{2,3,4} = 8/2

R_{2,3,4} = 4 Ω

R_{s} = R_{1} + R_{2,3,4} + R_{5}

R_{s} = 5 + 4 + 6

R_{s} = 15 Ω

The main current is

I_{s} = | V | |

R_{s} |

I_{s} = | 90 | |

15 |

I_{s} = 6 A

I_{2} = | R_{4}*I_{s} | |

R_{4} + R_{2,3} |

I_{2} = | 6*8 | |

16 |

I_{2} = 3 A

P_{2} = 3^{2}*5

_{}

P_{2} = 45 W

The current I5 is equal the current Is.

I_{5} = 6 A

P_{5} = 6^{2}*6

P_{5} = 216 W

P_{2} + P_{5} = 45 + 216

P_{2} + P_{5} = 261 W

The right answer is option C.

**Solution 2**

First, we must find the main current Is. Then we can calculate the power P_{1} and P_{2}.

The equivalent resistance of the circuit is

R_{s} = R_{1} + R_{2} + R_{3} + R_{4} + R_{5} + R_{6}

R_{s} = 10 + 6 + 4 + 8 + 3 + 9

R_{s} = 40 Ω

I_{s} = | 110 | |

40 |

I_{s} = 2,75 A

P_{2} = (I_{s})^{2}*R_{2}

P_{2 }= 7,56 * 6

P_{2} = 45, 36 W

P_{4} = (I_{s})^{2}*R_{4}

P_{4} = 7,56*8

P_{4} = 60,48 W

P_{2} + P_{4} = 45,36 + 60,48

P_{2} + P_{4} = 105,84 W

The right answer is option A

**Solution 3**

Let we find the current I_{1}.

P_{R1} = 63 W

P_{R1} = (I_{1})^{2}*R_{1}

63 = (I_{1})^{2}*7

(I_{1})^{2} = 9

(I_{1}) = 3 A

The voltage of the branching -1 is

V_{1} = I_{1}*(R_{1} + R_{2})

V_{1} = 3*10

V_{1 }= 30 V

The voltage of the branching -1 is equal to voltage of the branching -2.

The equivalent resistance of the branching -2 is

R_{3,4,5} = 4 + 8 + 3

R_{3,4,5} = 15 Ω

V_{R3-5} = V_{1}

V_{R3-5} = 30 V

I_{2} = | 30 | |

15 |

I_{2} = 2 A

I_{1} + I_{2} = 5 A

V_{R6} = 6*(I_{2} + I_{2})

V_{R6} = 6*5 = 30 V

The voltage of the circuit is

V_{s} = V_{1} + V_{6}

V_{s} = 30 + 30

V_{s} = 60 V

The right answer is option E

**Solution 4**

We need to find the current flows through R_{5}, for to find the power in R_{5}.

The current flowing through resistor R_{5} is I_{2}.

Let we find equivalent resistance of the branching-1

R_{2,3} = | 6*3 | |

9 |

R_{2,3} = 2 Ω

R_{1-4 }= 2 + 2 + 8

R_{1-4} = 12 Ω

Branching -1 gerilimi 72 Volttur. Çünkü kaynağa paralel bağlıdır. Bundan yararlanarak I_{1 } akımını bulabiliriz.

The voltage across branching-1 is 72 V. Because it is connected to the circuit in parallel. We can find the current I_{1} using this.

I_{1} = | 72 | |

12 |

I_{1} = 6 A

Let we find equivalent resistance of the branching -2 for to find the current I2.

R_{6,7} = | 4 | |

2 |

R_{6,7} = 2 Ω

R_{8,9,10} = | 6 | |

3 |

R_{8,9,10 }= 2 Ω

R_{5-10 }= 2 + 2 + 2

R_{5-10} = 6 Ω

The branch-2 has connected to the source in parallel and its voltage is 72 V.

I_{2} = | 72 | |

6 |

I_{2} = 12 A

Now, we can find power in the R_{5} .

P_{5} = (I_{2})^{2}*R_{5}

P_{5} = 144*2

P_{5} = 288

The right answer is option B

**Solution 5**

Let we find the equivalent resistance of the circuit.

R_{4,5} = 12 + 8

R_{4,5} = 20 Ω

R_{3-5} = | 5*20 | |

25 |

R_{3-5} = 4 Ω

R_{s} = R_{1} + R_{2} + R_{3-5}

R_{s} = 3 + 5 + 4

R_{s} = 12 Ω

I_{s} = | 48 | |

12 |

I_{s} = 4 A

I_{5} = | I_{s}*R_{3} | |

R_{4,5} + R_{3} |

I_{5} = | 4*5 | |

25 |

I_{5} = 0,8 A

P_{5} = (0,8)^{2}*R_{5}

P_{5} = 5,12 W

The right answer is option D.

**Solution 6**

We must find the current flowing through the R_{7} for to find the power in R_{7}.

We must find equivalent resistance of the circuit for to find the main current.

R_{3,4} = 2 Ω

R_{6,7} = | 12*6 | |

18 |

R_{6,7} = 4 Ω

R_{s} = R_{1} + R_{2} + R_{3,4} + R_{5} + R_{6,7}

R_{s} = 4 + 3 + 2 + 2 + 4 + 5

R_{s} = 20 Ω

I_{s} = | 120 | |

20 |

I_{s} = 6 A

I_{5} = Is

I_{5} = 6 A

I_{7} = | I_{5}*R_{6} | |

R_{6} + R_{7} |

I_{7} = | 6*6 | |

18 |

I_{7} = 2 A

P_{7} = (I_{7})^{2}*R_{7}

P_{7} = 4 * 12

P_{7} = 48 W

The right answer is option B

**Power Questions In Electric Circuits -1**

**Electric Circuits Questions And Explanatory Solutions**

**Power Questions In electric Circuits And Explanatory Solutions II**

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November 22 2018

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