Question

10. 6Ω and 12Ω resistors are connected in parallel. This combination is connected in series with a 10V battery and

6Ω resistor. What is the potential difference between the terminals of the 12Ω resistors?

(a) 14V (b) 10V (c) 16V (d) 4V​

Answer 1

${\bigstar}$ QUESTION:

10.6Ω and 12Ω resistors are connected in parallel. This combination is connected in series with a 10V battery and 6Ω resistor.

${\bigstar}$GIVEN:

Resistor A = 6Ω

Resistor B = 12Ω

Resistor Rx= 6Ω

${\bigstar}$TO FIND:

What is the potential difference between the terminals of the 12Ω resistors?

${\bigstar}$ ANSWER:

In parallel combination , voltage remains constant .

According to ohms law ,

$\boxed{\sf{ Voltage = current × resistance}}$

Current = voltage /resistance

Here,

Resistance (Rp) = 1/RA + 1/RB

= 1/6 + 1/12

= 12 + 6 / (6)(12)

= 18 / 72

= 1/4Ω

$\boxed{\sf{Rp = 4Ω}}$

R effective = Rx + Rp

= 6 + 4

= $\boxed{\sf{10Ω}}$1

Current = voltage /R effective

= 10/10

= $\boxed{\sf{1A}}$

Voltage A-B = V - Vx

= V - IxRx

= 10 - (1)(6)

= 10 - 6

= $\boxed{\sf{4V}}$