Question

Five resistances are connected in the shape of letter A as shown in
figure alongside. Determine the total resistance of the circuit.
​

Answer 1

GiveN :-

• Five resistances are connected in the shape of letter A as shown in
• figure alongside.

To FinD :-

• The total resistance of the circuit.

SolutioN :-

For the figure kindly refer to the attachment . So the circuit is in the shape of A and has 5 resistances connected to it . The resistances are 3Ω , 7Ω , 10Ω , and two 5Ω resistances . We need to find the net resistance . So here we can see that the 3Ω and 7Ω resistances are connected in series . So we know that when resistance are connected in series then the net resistance is the sum of individual resistances.

• So the net resistance will be :-

$\sf \to R_{(net)}= R_1+R_2 = (3+7)\Omega =\red{10\Omega }$

$\rule{200}2$

Now we see that the two 10Ω resistances are connected in parallel .

• So the net resistance will be :-

$\sf \to\dfrac{1}{ R_{(net)}}=\dfrac{1}{ R_{(net)}}+\dfrac{1}{R_2 }= \dfrac{10\Omega \times 10\Omega }{(10+10)\Omega }= \red{5\Omega}$

$\rule{200}2$

Now again we see that the three 5Ω resistances are connected in series .

• So the net resistance will be :-

$\sf\to R_{(net)}= R_1+R_2+R_3 \\\\\sf\to R_{(net)}= ( 5 + 5 + 5 )\Omega \\\\\sf\to\underset{\blue{\sf Required \ Resistance }}{\underbrace{\boxed{\pink{\frak{ Resistance_{(net)}= 15 \Omega }}}}}$