Question

For the circuit shown in the figure

• A. the current $I$ through the battery is $7.5 \,mA$
• B. the potential difference across $R_L$ is $18\, V$
• C. ratio of powers dissipated in $R_1 $ and $R_2$ is $3$
• D. if $R_1 $ and $ R_2$ are interchanged, magnitude of the power dissipated in $R_L$ will decrease by a factor of $9$

Hint:

\(\, \, \, \, \, \, \, p=\frac{V^2}{R} \, \, or \, \, P= V^2\)

Answer 1

The Correct Option is D

For the circuit shown in the figure

\(R_{total = 2 + \frac{6 \, \times \, 1.5}{6 \, + \, 1.5} } = 3.2k \Omega\)
\((A) \, I = \frac{25V}{3.2k \Omega} = 7.5mA = I_{R_1}\)
\(\, \, \, \, \, \, \, \, I_{R_2} = \bigg( \frac{R_L}{ R_L + R_2} \bigg) I\)
\(\, \, \, \, \, \, \, \, \, \, I = \frac{1.5}{7.5} \times 7.5 = 1.5mA\)
\(\, \, \, \, \, \, I_{R_2} = 6mA\)
\((B)V_{R_L} = (I_{R_L}) (R_L) = 9V\)
\((C) \frac{P_{R_1}}{P_{R_2}} = \frac{(I^2_{R_1} R_1)}{(I^2_{R_2})R_2} = \frac{(7.5)^2 (2)}{(1.5)^2(6)} = \frac{25}{3}\) 
(D) Now potential differences across \(R_L\) will be \(V_L = 24 \bigg[ \frac{6/7}{6 + 6/7} \bigg] = 3V\) Earlier it was 9 V 
Since, \(\, \, \, \, \, \, \, p=\frac{V^2}{R} \, \, or \, \, P= V^2\) 
In the new situation, the potential difference has been decreased three times. Therefore, if R₁ and R₂ are interchanged, magnitude of the power dissipated in R_L will decrease by the factor of 9.

Discover More Topics From This Chapter: Current Electricity

Answer 2

The Correct Answer is (D)

Real Life Applications

• To keep the same voltage level across all of the loads and components connected to it, a parallel circuit is employed.

• To avoid the effects of any one load harming the other as in a series circuit, a parallel circuit is utilized.
• When using a low voltage to drive several loads, a parallel circuit comes in quite handy.

Question can also be asked as

• What is the current flowing through each resistor?
• What is the voltage drop across each resistor?
• What is the total power dissipated by the circuit?
• What is the equivalent resistance of the circuit?
• What is the impedance of the circuit if it is connected to an AC source?
• What is the phase angle between the current and voltage in the circuit?
• What is the power factor of the circuit? What is the maximum current that the circuit can safely handle?