Question

Two resistors R1 = 6.7 Ω and R2 = 1.6 Ω are connected in parallel and a potential difference of ΔV = 12.0 V is imposed across them. Find the currents I1 and I2, and the current through the battery, I

Answer 1

I1 = 1.8A

I2 = 7.5A

I = 9.3A

Step-by-step explanation:

From the principle of basic electricity, when resistors are connected in parallel, the potential difference across them is the same but the current may vary depending on the value of the resistors.

Firstly we calculate the equivalent resistance in the circuit

1/R = 1/R1 + 1/R2

1/R = 1/6.7 + 1/1.6 = 0.774

R = 1/0.774 = 1.292Ω

Now let's calculate the total current flowing through the circuit (I)

V=IR

12=I × 1.292

I = 12/1.292 = 9.3A

The current flowing across R1 (I1) is calculated as

V = I1 × R1

12 = I1 × 6.7

I1 = 12/6.7

I1 = 1.8A

= 12/1.292 = 9.3A

The current flowing across R1 (I1) is calculated as

V = I1 × R1

12 = I1 × 6.7

I1 = 12/6.7

I1 = 1.8A

The current flowing across R2 is (I2) is calculated as

V = I2 × R2

12 = I2 × 1.6

I2 = 12/1.6

I2 = 7.5A

Confirming our overall current value

I1 + I2 = I

1.8A + 7.5A = 9.3A