Question

Two resistors 50 ohm and 100 ohm are connected across the same voltage
supply of 200 V. What net current does the power line draw ?​

Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• There are two resistors 50Ω and 100Ω.
• Voltage = 200 V.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

• The net current.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

You did not specify the connection, whether the resistors are connected in series or parallel, so I am doing both ways.

CASE 1: When resistors are connected in series.

We know that the total resistance in series:

$\sf{\red{R_s=R_1+R_2+R_3+R_4 .... R_n}}$

Here, R₁=50Ω and R₂=100Ω.

$\sf R_s=100+50$

$\boxed{\sf{\blue{R_s=150 \Omega}}}$

We know that by ohm's law:

$\sf I=\dfrac{V}{R}$

Here, V=200V, R=150Ω. Thus, substitute.

$\sf I=\dfrac{200}{150}$

$\boxed{\sf{\blue{I=1.33A}}}$

CASE 2: When resistors are connected in parallel.

We know that the total resistance in series:

$\sf{\red{\dfrac{1}{R_p}=\dfrac{1}{R_1} +\dfrac{1}{R_2} +\dfrac{1}{R_3} .....\dfrac{1}{R_n} }}$

Here, R₁=50Ω and R₂=100Ω.

$\sf \dfrac{1}{R_p}=\dfrac{1}{50} +\dfrac{1}{100}$

$\sf \dfrac{1}{R_s}= \dfrac{3}{100}$

$\boxed{\sf{\blue{R_s=\dfrac{100}{3} \Omega}}}$

Don't convert the fraction into a decimal here because it complicates our calculations.

We know that by ohm's law:

$\sf I=\dfrac{V}{R}$

Here, V=200V, R=100/3Ω. Thus, substitute.

$\sf I=\dfrac{200}{\dfrac{100}{3} }$

Denominator's denominator goes to the numerator.

$\sf I=\dfrac{200\times 3}{100}$

$\sf I=\dfrac{600}{100}$

$\boxed{\sf{\blue{I=6A}}}$

∴We observe two cases:

• When resistors are connected in series, current = 1.33A.
• When resistors are connected in parallel, current = 6A.