Question

Given a 10-V power supply, would a 20-ohm resistor and a 5-ohm resistor need to be arranged in parallel or in series to generate a current of 2.5 A? How much current would move through each resistor? In 3-4 sentences, answer each question and explain your answers

Answer 1

Answer:

The arrangement of the resistors to generate a current of 2.5 A is  a parallel arrangement and the current flowing the first resistor is  $I_1 = 0.5 \ A$   while the current flowing through the second resistor is  $I_2 = 2 \ A$

Explanation:

From the question we are told that

   The voltage is  $V = 10 \ V$

   The first resistor is  $R_1 = 20 \ \Omega$

    The second resistor is  $R_2 = 5 \ \Omega$

    The current is  $I = 2.5 \ A$

Generally the resistance of the circuit is mathematically evaluated as

      $R = \frac{V}{I}$

=>   $R = \frac{10 }{2.5}$

=>   $R = 4 \ \Omega$

When the given resistors are connected in series the resistance is  

     $R_e = R_1 + R_2$

=>  $R_e = 20 + 5$    

=>  $R_e = 25 \ \Omega$

Generally when the resistors are connected in parallel the resistance is  

      $R_e = \frac{R_1 * R_2}{R_1 + R_2}$    

=>    $R_e = \frac{20 * 5}{20 + 5}$    

=>    $R_e = 4 \ \Omega$

The current flowing through resistor 1 is mathematically represented as

      $I_1 = \frac{V}{R_1}$  

=>  $I_1 = \frac{10}{20 }$  

=>  $I_1 = 0.5 \ A$  

The current flowing through resistor 1 is mathematically represented as

      $I_2 = \frac{V}{R_2}$  

=>  $I_1 = \frac{5}{20 }$  

=>  $I_2 = 2 \ A$

The arrangement of the resistors to generate a current of 2.5 A is  a parallel arrangement and the current flowing the first resistor is  $I_1 = 0.5 \ A$   while the current flowing through the second resistor is  $I_2 = 2 \ A$