Question

[A] Write an expression for the equivalent resistance of three resistors connected in parallel.[ no derivation needed]

Answer 1

Answer:

1) R1 + ((R2 × R3)/(R2 + R3))

2) 0.5 A

3) 3.6 V

Explanation:

1) We can see that resistors R2 and R3 are in parallel.

Formula for sum of parallel resistors; 1/Rt = 1/R2 + 1/R3

Making Rt the subject gives;

Rt = (R2 × R3)/(R2 + R3)

Now, Resistor R1 is in series with this sum of R2 and R3. Thus;

Total resistance of circuit = R1 + ((R2 × R3)/(R2 + R3))

2) R_total = R1 + ((R2 × R3)/(R2 + R3))

We are given;

R1 = 7.2 Ω

R2 = 8 Ω

R3 = 12 Ω

R_total = 7.2 + ((8 × 12)/(8 + 12))

R_total = 7.2 + 4.8

R_total = 12 Ω

Formula for current is;

I = V/R

I = 6/12

I = 0.5 A

3) since current through the circuit is 0.5 and R1 is 7.2 Ω.

Thus, potential difference through R1 is;

V = IR = 0.5 × 7.2 = 3.6 V