A battery has an emf E and internal resistance r. A variable resistance R is connected across the terminals of the battery. Find the value of R such that (a) the current in the circuit id maximum (b) the potential difference across the terminals is maximum.
Text Solution
AI Generated Solution
To solve the problem, we need to analyze the circuit consisting of a battery with an electromotive force (emf) \( E \) and internal resistance \( r \), connected to a variable resistance \( R \). We will find the value of \( R \) for two scenarios: (a) when the current in the circuit is maximum, and (b) when the potential difference across the terminals is maximum.
### Step-by-Step Solution:
#### Part (a): Finding \( R \) for Maximum Current
1. **Understanding the Circuit**:
The total resistance in the circuit is the sum of the internal resistance \( r \) and the variable resistance \( R \). The current \( I \) flowing through the circuit can be expressed using Ohm's law:
...
Topper's Solved these Questions
CURRENT ELECTRICITY
PRADEEP|Exercise Conceptual Problems|3 Videos
CURRENT ELECTRICITY
PRADEEP|Exercise Very short Q/A|7 Videos
COMMUNICATION SYSTEMS
PRADEEP|Exercise MODEL TEST PAPER-2|9 Videos
DUAL NATURE OF RADIATION AND MATTER
PRADEEP|Exercise Exercise|191 Videos
Similar Questions
Explore conceptually related problems
A battery is of emt E and internal resistance r . The value of external resistance R so that the power across eternal resistance is maximum :
A battery of emf E has an internal resistance r. A variable resistacne R is connected to the terminals of the battery. A current i is drawn from the battery. V is the terminal potential difference. If R alone is gradually reduced to zero, which of the following best describes i and V?
A battery of emf E and internal resistance r is connected to a variable resistor R as shown in figure. Which one of the following is true ?
Shown n batteries connected to form a circuit. The resistances donote the internal resistances of the batteries which are related to the emf's as r_(i)=k(epsilon)_(i) where K is a constant. The solid dits represent the terminals of the batteries. Find (a)the current through the circuit and (b) the potential difference between the terminals of the ith battery.
A battery of emf E and internal resistance r is connected across a resistance R. Resistance R can be adjusted to any value greater than or equal to zero. A graph is plotted between the current passing through the resistance (I) and potential difference across the termainals of the battery (V). Maximum power developed across the resistance R is
Cell A has emf 2 E ad internal resistance 4 r. Cell B has emf E and internal resistance r. The negative of A is connected to the positive of B and a load resistance of R is connected across the battery formed. If the terminal potential difference across A is zero, then R is equal to
A battery of e.m.f. 10 V and internal resistance 0.5 ohm is connected across a variable resistance R . The value of R for which the power delivered in it is maximum is given by
PRADEEP-CURRENT ELECTRICITY-Problems for Practice (B)
