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Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B?
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Two resistors 15ohm and b ohm are connected in parallel . This combina...
Understanding the Circuit Configuration
In the given problem, we have two resistors: one is 15 ohms and the other is \( b \) ohms, connected in parallel. This parallel combination is then connected in series with a 50 ohm resistor to a 5-volt battery.
Applying Ohm's Law
The total current \( I \) in the circuit can be calculated using Ohm's Law:
\[
I = \frac{V}{R_{\text{total}}}
\]
Where \( V \) is the voltage (5V) and \( R_{\text{total}} \) is the total resistance in the circuit.
Finding Total Resistance
1. **Resistance of Parallel Combination:**
- The formula for two resistors in parallel is:
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{15} + \frac{1}{b}
\]
2. **Total Resistance in Series:**
- The total resistance \( R_{\text{total}} \) is:
\[
R_{\text{total}} = R_{\text{parallel}} + 50
\]
Given Current through b Ohm Resistor
- The current through the \( b \) ohm resistor is given as \( \frac{1}{3} \) A.
- Using the current division rule, the voltage across the parallel combination can be expressed as:
\[
V_{parallel} = I \times R_{\text{parallel}}
\]
Since total current \( I \) splits in parallel, we also know:
\[
I_{b} = \frac{V_{parallel}}{b} = \frac{1}{3}
\]
Calculating the Value of b
From the above, we can find \( V_{parallel} \):
1. **Voltage across parallel resistors:**
- Rearranging gives us:
\[
V_{parallel} = \frac{1}{3} \times b
\]
2. **Inserting into Total Voltage:**
- Since \( V_{total} = 5V \):
\[
5 = I \times (R_{\text{parallel}} + 50)
\]
3. **Final Steps:**
- Substitute \( R_{\text{parallel}} \) and \( I \) to find \( b \).
By solving these equations, we obtain the value of \( b \) which is approximately **30 ohms**.
In the given problem, we have two resistors: one is 15 ohms and the other is \( b \) ohms, connected in parallel. This parallel combination is then connected in series with a 50 ohm resistor to a 5-volt battery.
Applying Ohm's Law
The total current \( I \) in the circuit can be calculated using Ohm's Law:
\[
I = \frac{V}{R_{\text{total}}}
\]
Where \( V \) is the voltage (5V) and \( R_{\text{total}} \) is the total resistance in the circuit.
Finding Total Resistance
1. **Resistance of Parallel Combination:**
- The formula for two resistors in parallel is:
\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{15} + \frac{1}{b}
\]
2. **Total Resistance in Series:**
- The total resistance \( R_{\text{total}} \) is:
\[
R_{\text{total}} = R_{\text{parallel}} + 50
\]
Given Current through b Ohm Resistor
- The current through the \( b \) ohm resistor is given as \( \frac{1}{3} \) A.
- Using the current division rule, the voltage across the parallel combination can be expressed as:
\[
V_{parallel} = I \times R_{\text{parallel}}
\]
Since total current \( I \) splits in parallel, we also know:
\[
I_{b} = \frac{V_{parallel}}{b} = \frac{1}{3}
\]
Calculating the Value of b
From the above, we can find \( V_{parallel} \):
1. **Voltage across parallel resistors:**
- Rearranging gives us:
\[
V_{parallel} = \frac{1}{3} \times b
\]
2. **Inserting into Total Voltage:**
- Since \( V_{total} = 5V \):
\[
5 = I \times (R_{\text{parallel}} + 50)
\]
3. **Final Steps:**
- Substitute \( R_{\text{parallel}} \) and \( I \) to find \( b \).
By solving these equations, we obtain the value of \( b \) which is approximately **30 ohms**.
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Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B?
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Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B?.
Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors 15ohm and b ohm are connected in parallel . This combination is connected in Series to a 50hm resistor and a battery of e m f 5 volt . If the current through B Ohm resistor as 1/3 A find the value of B?.
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