# 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.

1
= 1
+ 1
 + 1 R3
R2
R1
Rs

1
1
+1
 + 1 6
3
6
Rs

1
 = 4 6
Rs

 Rs = 6 4

Rs = 1.5 Ω

The right answer is option C.

Solution 2

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

1
= 1
+1
 + 1 16
6
12
Rs

 Rs = 48 15

Rs = 3.2 Ω

The right answer is option B.

Solution 3

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

1
= 1
 + 1 +... R2
R1
Rs

If Rs = 2 Ω

1
=1
+1
 + 1 8
R2
8
2

1
=R2
+8
 + R2 8R2
8R2
8R2
2

1
 = 2R2 + 8 8R2
2

8R2 = 4R2 + 16

4R2 = 16

R2 = 4 Ω

The right answer is option D.

Solution 4

If we find the value of resistor R2, we can find its current.

The value of the resistor R2,

1
= 1
 + 1 R2
12
Rs

1
= 1
 + 1 R2
12
3

1
 = R2 + 12 12R2
3

12R2 = 3R2 + 36

9R2 = 36

R2 = 4 Ω

The total current of the circuit.

 Is = V Rs

 Is = 36 3

Is = 12 A

The current flow through resistor R2.

 IR2 = Is•R1 R1 + R2

 IR2 = 12•12 16

IR2 = 9 A

The right answer is option C.

Solution 5

The circuit have four of resistor connected in parallel.

1
1
+1
+1
 + 1 3
10
15
6
Rs

1
 = 20 30
Rs

Rs = 1,5 Ω

The right answer is option D.

Solution 6

The voltage across the resistor R2 will be 60 V whatever the value of the resistor R2.

The current flow through in resistor R2 is founds with equality of

 IR2 = V R2

For IR2 = 5 A,

 5 = 60 R2

R2 = 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.

 Rs = R n

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

For R = 108, n = 12,

 Rs = 108 12

Rs = 9 Ω

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

 Is = 72 9

Is = 8 A

The right answer is option B.

Solution 8

The total current of a circuit is founds as below.

 Is = V Rs

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

 Rs = 48 16

Rs = 3 Ω

1
=1
+1
 + 1 R3
8
12
3

1
= 2R3
+3R3
 + 24 24R3
24R3
24R3
3

1
 = 5R3 + 24 24R3
3

24R3 = 15R3 + 72

9R3 = 72

R3 = 8 Ω

The right answer is option B.

Solution 9

1
= 1
+1
 + 1 R3
10
10
4

1
 = 2R3 + 10 10R3
4

10R3 = 8R3 + 40

2R3 = 40

R3 = 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

 Rs = 60 = 6 Ω 10

The values of the resistor R2 and R3. The equivalent resistance of these resistors is

 R2,3 = 60 = 30Ω 2

The value of the equivalent resistance of R1 and R2,3 is

 R1,2,3 = 30 =15 Ω 2

If a resistor R4 is connect to the circuit, the equivalent resistance must be 6 Ohm.

1
= 1
 + 1 R4
15
6

1
= R4
 + 15 15R4
15R4
6

1
 = R4 + 15 R4
6

15R4 = 6R4 + 90

9R4 = 90

R4 = 10 Ω

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

The right answer is option C

The questions

Series Connected Resistor Questions

Parallel Circuits Subject Expression

RISE KNOWLEDGE

28/10/2018

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