Question

Four resistors are connected to a battery as shown in the figure. The current in the battery is I, the battery emf is ? = 11.55 V, and the resistor values are R1 = R, R2 = 2R, R3 = 4R, R4 = 3R. Find the voltages across each resistor.

v1=

v2=

v3=

v4=

Answer 1

Here

Net resistance = 3R

Therefore

Current = 11.55/3R

= 3.85/R

v1 = 3.85 V

v2 = 3.85/3R * 2R

= 2.5667 V

v3 = 3.85/3R *4R

= 5.133 V

v4 = 7.7 V

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) = 11.55 / (3R) 

= 3.85 / R  amps.

Voltage , v1, across resistor R1 

= I * R 

= 3.85 / R  * R 

= 3.85 volts .

So, voltage across resistors (R2 + R3)  

= 11.55 - 3.85 = 7.7 volts.

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

So, current through (R2 + R3) 

= 7.7 / 6R 

= 1.28333 / R

So, voltage v2 across R2 

= 1.28333 / R * 2R 

= 2.567 volts 

So, voltage across R3 

= 7.7 - 2.567 

= 5.133 volts (ANSWER).

Voltage across R4 

= Voltage across (R2 + R3)

= 7.7 volts (ANSWER).

So, 

 v1 = 3.85 volts 

v2 = 2.567 volts 

v3 = 5.133 volts  

v4 = 7.7 volts 

(ANSWER).