Question

Two resistors are joined in series, then their equivalent resistance is $90\Omega$. When the same resistors are joined in parallel, the equivalent resistance is $20\Omega$.
The resistances of the two resistors will be :

• A. $70\Omega ,20\Omega$
• B. $80\Omega ,10\Omega$
• C. $60\Omega ,30\Omega$
• D. $50\Omega ,40\Omega$

Answer 1

The correct option is C $60\Omega ,30\Omega$

Answer is C.

Components connected in parallel are connected so the same voltage is applied to each component. In a parallel circuit, the voltage across each of the components is the same, and the total current is the sum of the currents through each component. To find the total resistance of all components, the reciprocals of the resistances of each component is added and the reciprocal of the sum is taken. Hence, the Total resistance will always be less than the value of the smallest resistance. That is, $\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}...\frac{1}{R_n},R={R_{total}}^{-1}$. . Components connected in series are connected along a single path, so the same current flows through all of the components. The current through each of the components is the same, and the voltage across the circuit is the sum of the voltages across each component. In a series circuit, every device must function for the circuit to be complete. One bulb burning out in a series circuit breaks the circuit. A circuit composed solely of components connected in series is known as a series circuit.The total resistance of resistors in series is equal to the sum of their individual resistances. That is, $R_{total}=R_1+R_2...R_n$.
In this case, $R_1+R_2=90ohms$ and $\frac{1}{R_1}+\frac{1}{R_2}=20ohms$.
Solving these 2 equations for $R_{1}and{R}_2$
we get,
$R_1=60ohmsand{R}_2=30ohms$.