Question

In the given circuit calculate
(i) the total resistance
(ii) the current through each resistance
(iii) the P.D. across each resistor.

Answer 1

Given:

Circuit is provided in diagram.

To find:

• Total resistance
• Current through each resistance
• Potential Difference across each resistance

Diagram:

The circuit can be reimagined as attached in hand-drawn diagram.

Calculation:

The upper three 10 ohm are in series and the lower left side 10 ohm is in parallel with them.

$\therefore \: r_{eq} = \dfrac{10 \times 30}{10 + 30}$

$\implies\: r_{eq} = \dfrac{300}{40}$

$\implies\: r_{eq} = \dfrac{30}{4}$

$\implies\: r_{eq} = 7.5 \: ohm$

So, equivalent resistance of the circuit is 7.5 Ohm.

Now, current through the upper three 10 ohm resistors are :

$\therefore \: i_{1} = \dfrac{volt}{r}$

$\implies\: i_{1} = \dfrac{3}{30}$

$\implies\: i_{1} = 0.1 \: amp$

Now, current through lower 10 ohm resistor is:

$\therefore \: i_{2} = \dfrac{volt}{r}$

$\implies\: i_{2} = \dfrac{3}{10}$

$\implies\: i_{2} = 0.3 \: amp$

Potential difference across the upper three resistors will be equally divided as :

$\therefore \: V_{upper} = \dfrac{3}{3} = 1 \: volt$

For lower resistor:

$\therefore \: V_{lower} = \dfrac{3}{1} = 3\: volt$

Hope It Helps.