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Three resistors are connected in parallel. If placed in a circuit with a 12-volt power supply. Determine the equivalent resistance (rounded to the nearest hundredth), the total circuit current (rounded to the nearest hundredth), and the voltage drop across and current in each resistor (round to the nearest hundredth).

Answer :

ONYEBUCHINNAJIGO

(a) The equivalent resistance of three parallel resistors is (R₁R₂R₃)/(R₁R₂ + R₁R₃ + R₂R₃).

(b) The total circuit current is 12/R.eq.

(c) The voltage drop across and current in each resistor is IR₁, IR₂ and IR₃.

Equivalent resistance of three parallel resistors

The equivalent resistance of three parallel resistors is calculated as follows;

  • Let the first resistor = R₁
  • Let the second resistor = R₂
  • Let the third resistor = R₃

[tex]\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_2}\\\\R_{eq} = \frac{R_1R_2R_3}{R_1R_2 + R_2R_3 + R_1R_3}[/tex]

Total Circuit Current

The total circuit current is calculated as follows;

V = IR

[tex]I= \frac{V}{R_{eq}} = \frac{12 \ V}{R_{eq}}[/tex]

Voltage drop in each resistor

Voltage drop in resistor 1 = IR₁

Voltage drop in resistor 2 = IR₂

Voltage drop in resistor 3 = IR₃

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