Question

The drawing shows three different resistors in two different circuits. The battery has a voltage of 20 V, and the resistors have values of R1 = 50 Ω, R2 = 25 Ω, and R3 = 10 Ω. 

(a) For the circuit on the left, determine the current through each resistor. 

(b) For the circuit on the left, determine the voltage across each resistor. 

(c) Which one has the largest voltage drop? Think why. Ask an instructor if you are not sure. 

(d) What is the total current for the circuit on the right? 

(e) Which of the two circuits (a or b) will have a greater equivalent resistance? 

Answer 1

Answer 2

SOLUTION :

a. 

For left circuit (series circuit) , current through each resistor 

= V(R1 + R2 + R3)

= 20/(50+25+10)

= 0.235 Amp. (ANSWER).

b.

Voltage drop across R1 = IR1 = 0.235*50 = 11.75 V (ANSWER)

Voltage drop across R2 = IR2 = 0.235*25 = 5.88 V (ANSWER)

Voltage drop across R1 = IR1 = 0.235*10 = 2.35 V (ANSWER)

c. 

Largest voltage drop is across 50 Ω resistor. It is so as it has the highest resistance in the circuit.  (ANSWER)

d.

Total current in the right circuit

= V / ( (R1R2 + R2R3 + R3R1)/(R1*R2*R3))

= 20/((1250 + 250 + 500)/85)

= 20 / 23.5294

= 0.85 Amp. (ANSWER)

e.

Circuit on the left has greater resistance compared to the of the right circuit.

(ANSWER)