# 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 R5 is P5.

P5 = (I5)2*R5

P5 = (I5)2*6

The power in the R2 is P2.

P2 = (I2)2*R2

P2 = (I2)2*5

The equivalent resistance of the circuit.

R2,3 = 5 + 3

R2,3 = 8 Ω

The R2,3 and R4 are parallel.

R2,3,4 = 8/2

R2,3,4 = 4 Ω

Rs = R1 + R2,3,4 + R5

Rs = 5 + 4 + 6

Rs = 15 Ω

The main current is

 Is = V Rs

 Is = 90 15

Is = 6 A

 I2 = R4*Is R4 + R2,3

 I2 = 6*8 16

I2 = 3 A

P2 = 32*5

P2 = 45 W

The current I5 is equal the current Is.

I5 = 6 A

P5 = 62*6

P5 = 216 W

P2 + P5 = 45 + 216

P2 + P5 = 261 W

The right answer is option C.

Solution 2 First, we must find the main current Is. Then we can calculate the power P1 and P2.

The equivalent resistance of the circuit is

Rs = R1 + R2 + R3 + R4 + R5 + R6

Rs = 10 + 6 + 4 + 8 + 3 + 9

Rs = 40 Ω

 Is = 110 40

Is = 2,75 A

P2 = (Is)2*R2

P2 = 7,56 * 6

P2 = 45, 36 W

P4 = (Is)2*R4

P4 = 7,56*8

P4 = 60,48 W

P2 + P4 = 45,36 + 60,48

P2 + P4 = 105,84 W

The right answer is option A

Solution 3 Let we find the current I1.

PR1 = 63 W

PR1 = (I1)2*R1

63 = (I1)2*7

(I1)2 = 9

(I1) = 3 A

The voltage of the branching -1 is

V1 = I1*(R1 + R2)

V1 = 3*10

V1 = 30 V

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

The equivalent resistance of the branching -2 is

R3,4,5 = 4 + 8 + 3

R3,4,5 = 15 Ω

VR3-5 = V1

VR3-5 = 30 V

 I2 = 30 15

I2 = 2 A

I1 + I2 = 5 A

VR6 = 6*(I2 + I2)

VR6 = 6*5 = 30 V

The voltage of the circuit is

Vs = V1 + V6

Vs = 30 + 30

Vs = 60 V

The right answer is option E

Solution 4 We need to find the current flows through R5, for to find the power in R5.

The current flowing through resistor R5 is I2.

Let we find equivalent resistance of the branching-1

 R2,3 = 6*3 9

R2,3 = 2 Ω

R1-4 = 2 + 2 + 8

R1-4 = 12 Ω

Branching -1 gerilimi 72 Volttur. Çünkü kaynağa paralel bağlıdır. Bundan yararlanarak I1  akımını bulabiliriz.

The voltage across branching-1 is 72 V. Because it is connected to the circuit in parallel. We can find the current I1 using this.

 I1 = 72 12

I1 = 6 A

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

 R6,7 = 4 2

R6,7 = 2 Ω

 R8,9,10 = 6 3

R8,9,10 = 2 Ω

R5-10 = 2 + 2 + 2

R5-10 = 6 Ω

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

 I2 = 72 6

I2 = 12 A

Now, we can find power in the R5 .

P5 = (I2)2*R5

P5 = 144*2

P5 = 288

The right answer is option B

Solution 5 Let we find the equivalent resistance of the circuit.

R4,5 = 12 + 8

R4,5 = 20 Ω

 R3-5 = 5*20 25

R3-5 = 4 Ω

Rs = R1 + R2 + R3-5

Rs = 3 + 5 + 4

Rs = 12 Ω

 Is = 48 12

Is = 4 A

 I5 = Is*R3 R4,5 + R3

 I5 = 4*5 25

I5 = 0,8 A

P5 = (0,8)2*R5

P5 = 5,12 W

The right answer is option D.

Solution 6 We must find the current flowing through the R7 for to find the power in R7.

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

R3,4 = 2 Ω

 R6,7 = 12*6 18

R6,7 = 4 Ω

Rs = R1 + R2 + R3,4 + R5 + R6,7

Rs = 4 + 3 + 2 + 2 + 4 + 5

Rs = 20 Ω

 Is = 120 20

Is = 6 A

I5 = Is

I5 = 6 A

 I7 = I5*R6 R6 + R7

 I7 = 6*6 18

I7 = 2 A

P7 = (I7)2*R7

P7 = 4 * 12

P7 = 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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