For the circuit shown in the figure
Show Hint
\(\, \, \, \, \, \, \, p=\frac{V^2}{R} \, \, or \, \, P= V^2\)
- the current $I$ through the battery is $7.5 \,mA$
- the potential difference across $R_L$ is $18\, V$
- ratio of powers dissipated in $R_1 $ and $R_2$ is $3$
- if $R_1 $ and $ R_2$ are interchanged, magnitude of the power dissipated in $R_L$ will decrease by a factor of $9$
The Correct Option is D
Approach Solution - 1
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 RL will decrease by the factor of 9.
Discover More Topics From This Chapter: Current Electricity
Approach Solution -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
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Concepts Used:
Current Electricity
Current electricity is defined as the flow of electrons from one section of the circuit to another.
Types of Current Electricity
There are two types of current electricity as follows:
Direct Current
The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.
Alternating Current
The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.