A resistor is an electrical component that provides electrical resistance or limits the flow of current in a circuit. For calculating resistance (R) values of voltage(V) and current (I) should be known.
The correct quantities are (a) 12.5 ohms, (b) 10A (c) 6.25 A, 1.25A, 2.5A (d) 125 V (e) 781.25 W, 156.25 W and 312.5 W.
The calculations are as follows:
Given,
(a) Equivalent resistance in parallel resistor:
[tex]\rm \dfrac{1}{Req} = \dfrac{1} {R1} + \dfrac{1} {R2} + \dfrac{1} {R3}[/tex]
[tex]\rm \dfrac{1}{Req} = \dfrac{1} {20} + \dfrac{1} {100} + \dfrac{1} {50}[/tex]
So,
[tex]\rm \dfrac{1}{Req} = \dfrac{5} {100} + \dfrac{1} {100} + \dfrac{2} {100}[/tex]
[tex]\rm \dfrac{1}{Req} = \dfrac{8} {100}[/tex]
Req = 12.5 ohms
(b) Current can be calculated using the formula:
V = IR
Where,
V = 125 V
I = ?
R = 12.5 ohms
Substituting values in equation:
[tex]\rm 125 = I \times 12.5[/tex]
[tex]\rm I = \dfrac {125 }{12.5} \\\\I = 10 A[/tex]
Therefore, current is 10 Amperes.
(c) Current through each resistor:
Given,
V = 125 V
I = ?
[tex]\rm 125 = I \times 20\\\\I1 = 6.25 A[/tex]
[tex]\rm 125 = I \times 100\\\\I2= 1.25A[/tex]
[tex]\rm 125 = I \times 50 \\\\I3= 2.5 A[/tex]
(d) Voltage drop across each resistor in a parallel circuit can be calculated by:
For parallel:
Given from (c)
I1 = 6.25
I2= 1.25 A
I3 = 2.5 A
[tex]\rm V1 = 6.25 \times 20\\V 1 = 125[/tex]
[tex]\rm V2 = 1.25 \times 100\\ V2= 125[/tex]
[tex]\rm V3 = 2.5 \times 50\\ V3= 125[/tex]
(e) Power dissipated by each source can be calculated by the following formula:
Given,
V = 125 V
[tex]\rm P = \dfrac {V^{2}}{ R}[/tex]
Resistor 1:
[tex]\rm P = \dfrac {(125)^ 2 }{ 20}\\\\P1 = 781.25 W[/tex]
Resistor 2:
[tex]\rm P = \dfrac {(125)^ 2 }{ 100}\\\\P2 = 156.25 W[/tex]
Resistor 3:
[tex]\rm P = \dfrac {(125)^ 2 }{ 50}\\\\P3 = 312.5 W[/tex]
Therefore, (a) 12.5 ohms, (b) 10A (c) 6.25 A, 1.25A, 2.5A (d) 125 V (e) 781.25 W, 156.25 W and 312.5 W.
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