Question

A series RC circuit contains two resistors and two capacitors. The resistors are 39 ohms and 56 ohms. The capacitors have capacitive reactances of 80 ohms and 40 ohms. When calculating the circuit values, the total resistance used is:_______
a. 215 ohms
b. 95 ohms
c. 25 ohms
d. 120 ohms

Answer 1

Answer:

The  correct option is b

Explanation:

From the question we are told that

    The resistance of the first resistor is  $R_1 = 39 \ \Omega$

     The resistance of the second resistor is  $R_2 = 56 \ \Omega$

      The capacitive reactance of the first capacitor is $jX_{c_1 } = 80 \ \Omega$

       The capacitive reactance of the first capacitor is $jX_{c_2 } = 40 \ \Omega$

Generally given that the resistors are connected in parallel , their equivalent resistance is  

            $R_e = R_1 +R_2$

=>         $R_e = 39 + 56$

=>         $R_e = 95 \ \Omega$

Generally given that the capacitors are connected in parallel , their equivalent capacitive reactance  is  

          $jX_e = jX_{c_1} + jX_{c_2}$

=>       $jX_e = 80 + 40$

=>       $jX_e = 120$

Hence the impedance of the circuit is  

         $Z = R_e - jX_e$        

=>      $Z = 95 - j120$          

Generally from the impedance equation , the total used resistance is  

       $R_e = 95 \ \Omega$