Question

Four resistors are connected to a battery as shown in the figure. The current through the battery is I, the battery's electromotive force (emf) is ℰ=2.20 V, and the resistor values are R1=R, R2=2 R, R3=4 R, and R4=3 R. 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) = 2.20 / (3R) 

= 0.7333 / R  amps.

Voltage , v1, across resistor R1 

= I * R 

= 0.7333 / R  * R 

= 1.467 volts .

So, voltage across resistors (R2 + R3)  

= 2.20 - 1.467 = 0.733 volts.

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

So, current through (R2 + R3) 

= 0.733 / (6R)

= 0.122 / R

So, voltage v2 across R2 

= 0.122 / R * 2R 

= 0.244  volts 

So, voltage v3 across R3 

= 0.733 - 0.244 

= 0.489  volts (ANSWER).

Voltage v4 across R4 

= Voltage across (R2 + R3)

= 0.733 volts (ANSWER).

So, 

 v1 = 1.467 volts 

v2 = 0.244 volts 

v3 = 0.489 volts  

v4 = 0.733 volts 

(ANSWER).