Question

Two resistors of R1 = 30Ω and R2 = 21Ω are connected in parallel across a battery of voltage 10V. Determine (a) the total current flowing through the circuit; b) current flowing through individual resistors c) voltage across each resistor.

Answer 1

a) 0.81 A

b) 0.33 A , 0.48 A

c) 10 Volts , 10 volts

Step-by-step explanation:

`R_(1)` = 30 Ω

`R_(2)` = 21 Ω

`V` = Voltage of the battery = 10 Volts

a)

Parallel combination of resistance is given as

`R = (R_(1)R_(2))/(R_(1) + R_(2))`

`R = ((30) (21))/(30 + 21)`

`R = 12.4` Ω

`i` = Total current flowing through the circuit

Total current flowing through the circuit is given as

`i = (V)/(R)`

`i = (10)/(12.4)`

`i = 0.81` A

b)

In parallel, Voltage remain same.

`V_(1)` = Potential difference across R₁ = 10 Volts

`V_(2)` = Potential difference across R₂ = 10 Volts

Current flowing through individual resistors is given as

`i_(1) = (V_(1))/(R_(1))`

`i_(1) = (10)/(30)`

`i_(1) = 0.33` A

`i_(2) = (V_(2))/(R_(2))`

`i_(2) = (10)/(21)`

`i_(2) = 0.48` A

c)

In parallel, Voltage remain same, hence

`V_(1)` =
`V_(2)` = 10 Volts