Question

Consider the circuit shown in the figure below.(Assume R_1 = 11.5 ohm and R_2 = 3.50 ohm.) v find the potential difference between points a and b. Find the current in the 20.0-ohm resistor. A

Answer 1

a) The total voltage 25 V is dropped across the resistance R₁and the combination of parallel resistance
The net parallel resistance is
1 / R_p  = 1 / R₁ + 1/ R₂  + 1 /(R₂ + 20)
1 / R_p  = 1/ 11.5 + 1/3.5 + 1 / (3.5 + 20)
R_p = 2.41 $\Omega$
The total current passing through the resistors R₁ and R_p  
I = V / (R₁ + R_p)
I = 25 / (11.5 + 2.41)
I = 1.797 A
The potential difference across the resistance R_p is
V_ab  = I x R_p  
V_ab  = 1.797 x 2.41
V_ab  = 4.332 V
b) The current through R₂and the 20 $\Omega$ resistor is
I_R  = V_ab / (R₂  + 20)
I_R  =   4.332 V / 23.5
I_R  = 0.184 A
This will be the current through the 20 $\Omega$ resistor (The same current passes through the resistors R₂ and 20 $\Omega$)