Question

Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emfis E= 6.90 V, and the resistor values are R1=R, R2 = 2R, R3 = 4R, R4=3R. Find the voltages across each resistor. 

Answer 1

Answer 2

SOLUTION :

Equivalent of all resistors connected to the battery 

= R1 + (1 / (1/(R2 + R3) + 1/R4) 

= R + ( 1/(2R + 4R) + 1/(3R) )

= R + 1/( ( 1 + 2) / (6R)) 

= R + 1/(1/(2R))

= R + 2R

= 3R 

So, current flow from the battery, I 

= V / (3R) = 6.90 / (3R) 

= 2.30/ R  amps.

Voltage , v1, across resistor R1 

= I * R 

= 2.30 / R  * R 

= 2.30 volts .

So, voltage across resistors (R2 + R3)  

= 6.90 - 2.30 = 4.60 volts.

But, R2 + R3 = 2R + 4R = 6R

So, current through (R2 + R3) 

= 4.60 / (6R) 

= 0.7667 / R

So, voltage v2 across R2 

= 0.7667 / R * 2R 

= 1. 533 volts 

So, voltage across R3 

= 4.60 - 1.533 

= 3.067 volts (ANSWER).

Voltage across R4 

= Voltage across (R2 + R3)

= 4.60 volts (ANSWER).

So, 

 v1 = 2.30 volts 

v2 = 1.533 volts 

v3 = 4.067 volts  

v4 = 4.60 volts 

(ANSWER).