Question

In a circuit having 2 resistances of 30Ω and 30Ω are connected in parallel to a 240 V supply. Find the current flowing through the circuit.​

Answer 1

Answer:

Given :-

• In a circuit having two resistances of 30Ω and 30Ω are connected in parallel to a 240 V supply.

To Find :-

• What is the current flowing through the circuit.

Formula Used :-

$\clubsuit$ Equivalent Resistance for parallel connection formula :

$\mapsto \sf\boxed{\bold{\pink{\dfrac{1}{R_{eq}} =\: \dfrac{1}{R_1} + \dfrac{1}{R_2} + . . . . + \dfrac{1}{R_n}}}}$

$\clubsuit$ Voltage Formula :

$\mapsto \sf\boxed{\bold{\pink{V =\: IR}}}$

where,

• V = Voltage
• I = Current
• R = Resistance

Solution :-

First, we have to find the resistance :

Given :

• R₁ = 30Ω
• R₂ = 30Ω

According to the question by using the formula we get,

$\implies \sf \dfrac{1}{R_{eq}} =\: \dfrac{1}{30} + \dfrac{1}{30}$

$\implies \sf \dfrac{1}{R_{eq}} =\: \dfrac{1 + 1}{30}$

$\implies \sf \dfrac{1}{R_{eq}} =\: \dfrac{2}{30}$

By doing cross multiplication we get,

$\implies \sf 2 \times R_{eq} =\: 30 \times 1$

$\implies \sf 2R_{eq} =\: 30$

$\implies \sf R_{eq} =\: \dfrac{\cancel{30}}{\cancel{2}}$

$\implies \sf R_{eq} =\: \dfrac{15}{1}$

$\implies \sf\bold{\purple{R_{eq} =\: 15\: \Omega}}$

Now, we have to find the current flowing through the circuit :

Given :

• Voltage (V) = 240 V
• Resistance (R) = 15 Ω

According to the question by using the formula we get,

$\longrightarrow \bf V =\: IR$

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

$\bigstar\: \: \sf\bold{\green{Current =\: \dfrac{Voltage}{Resistance}}}\: \: \bigstar$

$\longrightarrow \sf Current =\: \dfrac{\cancel{240}}{\cancel{15}}$

$\longrightarrow \sf Current =\: \dfrac{16}{1}$

$\longrightarrow \sf\bold{\red{Current =\: 16A}}$

${\small{\bold{\underline{\therefore\: The\: current\: flowing\: through\: the\: circuit\: is\: 16A\: .}}}}$